### Equilibrium configurations of epitaxially strained crystalline films

- Series
- PDE Seminar
- Time
- Tuesday, August 19, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Giovanni Leoni – Carnegie Mellon University, Pittsburgh

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- Series
- PDE Seminar
- Time
- Tuesday, August 19, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Giovanni Leoni – Carnegie Mellon University, Pittsburgh

In this talk we will discuss some recent existence and regularity results for equilibrium configurations of epitaxially strained crystalline films.

- Series
- Analysis Seminar
- Time
- Monday, August 25, 2008 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Maria Clara Nucci – Dept. of Mathematics and Informatics, University of Perugia

In any standard course of Analytical Mechanics students are indoctrinated that a Lagrangian have a profound physical meaning (kinetic energy minus potential energy) and that Lagrangians do not exist in the case of nonconservative system. We present an old and regretfully forgotten method by Jacobi which allows to find many nonphysical Lagrangians of simple physical models (e.g., the harmonic oscillator) and also of nonconservative systems (e.g., the damped oscillator). The same method can be applied to any equation of second-order, and extended to fourth-order equations as well as systems of second and first order. Examples from Physics, Number Theory and Biology will be provided.

- Series
- CDSNS Colloquium
- Time
- Monday, August 25, 2008 - 16:30 for 2 hours
- Location
- Skiles 269
- Speaker
- Francisco J. Beron-Vera – Marine &amp; Atmospheric Science, University of Miami

The connection between transport barriers and potential vorticity (PV) barriers in PV-conserving flows is investigated with a focus on zonal jets in planetary atmospheres. A perturbed PV-staircase model is used to illustrate important concepts. This flow consists of a sequence of narrow eastward and broad westward zonal jets with a staircase PV structure; the PV-steps are at the latitudes of the cores of the eastward jets. Numerically simulated solutions to the quasigeostrophic PV conservation equation in a perturbed PV-staircase flow are presented. These simulations reveal that both eastward and westward zonal jets serve as robust meridional transport barriers. The surprise is that westward jets, across which the background PV gradient vanishes, serve as robust transport barriers. A theoretical explanation of the underlying barrier mechanism is provided, which relies on recent results relating to the stability of degenerate Hamiltonians under perturbation. It is argued that transport barriers near the cores of westward zonal jets, across which the background PV gradient is small, are found in Jupiter's midlatitude weather layer and in the Earth's summer hemisphere subtropical stratosphere.

- Series
- PDE Seminar
- Time
- Tuesday, August 26, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Eldad Haber – Mathematics &amp; Computer Science, Emory University

Optimization problems with PDE constraints are commonly solved in different areas of science and engineering. In this talk we give an introduction to this field. In particular we discuss discretization techniques and effective linear and nonlinear solvers. Examples are given from inverse problems in electromagnetics.

- Series
- Research Horizons Seminar
- Time
- Wednesday, August 27, 2008 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Tom Trotter, Teena Carroll, Luca Dieci – School of Mathematics, Georgia Tech

* Dr. Trotter: perspective of the hiring committee with an emphasis on research universities.
* Dr. Carroll: perspective of the applicant with an emphasis on liberal arts universities.
* Dr. Dieci: other advice, including non-academic routes.

- Series
- Graph Theory Seminar
- Time
- Thursday, August 28, 2008 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Sergey Norin – Mathematics, Princeton University

The problem of generating random integral tables from the set of all nonnegative integral tables with fixed marginals is of importance in statistics. The Diaconis-Sturmfels algorithm for this problem performs a random walk on the set of such tables. The moves in the walk are referred to as Markov bases and correspond to generators of a certain toric ideal. When only one and two-way marginals are considered, one can naturally associate a graph to the model. In this talk, I will present a characterization of all graphs for which the corresponding toric ideal can be generated in degree four, answering a question of Develin and Sullivant. I will also discuss some related open questions and demonstrate applications of the Four Color theorem and results on clean triangulations of surfaces, providing partial answers to these questions. Based on joint work with Daniel Kral and Ondrej Pangrac.

- Series
- Stochastics Seminar
- Time
- Thursday, August 28, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Mikhail Lifshits – School of Mathematics, Georgia Tech

We consider a random field of tensor product type X and investigate the quality of approximation (both in the average and in the probabilistic sense) to X by the processes of rank n minimizing the quadratic approximation error. Most interesting results are obtained for the case when the dimension of parameter set tends to infinity. Call "cardinality" the minimal n providing a given level of approximation accuracy. By applying Central Limit Theorem to (deterministic) array of covariance eigenvalues, we show that, for any fixed level of relative error, this cardinality increases exponentially (a phenomenon often called "intractability" or "dimension curse") and find the explosion coefficient. We also show that the behavior of the probabilistic and average cardinalities is essentially the same in the large domain of parameters.

- Series
- Combinatorics Seminar
- Time
- Friday, August 29, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Kevin Costello – School of Mathematics, Georgia Tech

Let f be a polynomial or multilinear form in a large number of variables. A basic question we can ask about f is how dispersed it becomes as the number of variables increases. To be more concrete: If we randomly (and independently) set each entry to be either 1 or -1, what is the largest concentration of the output of f on any single value, assuming all (or most) of the coefficients of f are nonzero? Can we somehow describe the structure of those forms which are close to having maximal concentration? If f is a linear polynomial, this is a question originally examined by Littlewood and Offord and answered by Erdos: The maximal concentration occurs when all the nonzero coefficients of f are equal. Here we will consider the case where f is a bilinear or quadratic form.

- Series
- PDE Seminar
- Time
- Tuesday, September 2, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Zhiwu Lin – School of Mathematics, Georgia Tech

Shear flow instability is a classical problem in hydrodynamics. In particular, it is important for understanding the transition from laminar to turbulent flow. First, I will describe some results on shear flow instability in the setting of inviscid flows in a rigid wall. Then the effects of a free surface (or water waves) and viscosity will be discussed.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, September 3, 2008 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Annalisa Bracco – School of Earth &amp; Atmospheric Sciences, Georgia Tech

In the ocean, coherent vortices account for a large portion of the ocean turbulent kinetic energy and their presence significantly affects the dynamics and the statistical properties of ocean flows, with important consequences on transport processes. Mesoscale vortices also affect the population dynamics of phyto- and zooplankton, and are associated with secondary currents responsible for localized vertical fluxes of nutrients. The fact that the nutrient fluxes have a fine spatial and temporal detail, generated by the eddy field, has important consequences on primary productivity and the horizontal velocity field induced by the eddies has been suggested to play an important role in determining plankton patchiness. Owing to their trapping properties, vortices can also act as shelters for temporarily less-favoured planktonic species. In this contribution, I will review some of the transport properties associated with coherent vortices and their impact on the dynamics of planktoni ecosystems, focusing on the simplified conceptual model provided by two-dimensional turbulence.

- Series
- Research Horizons Seminar
- Time
- Wednesday, September 3, 2008 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Robin Thomas – School of Mathematics, Georgia Tech

I will explain and prove a beautiful and useful theorem of Alon and Tarsi that uses multivariate polynomials to guarantee, under suitable hypotheses, the existence of a coloring of a graph. The proof method, sometimes called a Combinatorial Nullstellensatz, has other applications in graph theory, combinatorics and number theory.

- Series
- Stochastics Seminar
- Time
- Thursday, September 4, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Heinrich Matzinger – School of Mathematics, Georgia Tech

A common subsequence of two sequences X and Y is a sequence which is a subsequence of X as well as a subsequence of Y. A Longest Common Subsequence (LCS) of X and Y is a common subsequence with maximal length. Longest Common subsequences can be represented as alignments with gaps where the aligned letter pairs corresponds to the letters in the LCS. We consider two independent i.i.d. binary texts X and Y of length n. We show that the behavior of the the alignment corresponding to the LCS is very different depending on the number of colors. With 2-colors, long blocks tend to be aligned with no gaps, whilst for four or more colors the opposite is true. Let Ln denote the length of the LCS of X and Y. In general the order of the variance of Ln is not known. We explain how a biased affect of a finite pattern can influence the order of the fluctuation of Ln.

- Series
- Combinatorics Seminar
- Time
- Friday, September 5, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Ernie Croot – School of Mathematics, Georgia Tech

Let A be a set of n real numbers. A central problem in additive combinatorics, due to Erdos and Szemeredi, is that of showing that either the sumset A+A or the product set A.A, must have close to n^2 elements. G. Elekes, in a short and brilliant paper, showed that one can give quite good bounds for this problem by invoking the Szemeredi-Trotter incidence theorem (applied to the grid (A+A) x (A.A)). Perhaps motivated by this result, J. Solymosi posed the following problem (actually, Solymosi's original problem is slightly different from the formulation I am about to give). Show that for every real c > 0, there exists 0 < d < 1, such that the following holds for all grids A x B with |A| = |B| = n sufficiently large: If one has a family of n^c lines in general position (no three meet at a point, no two parallel), at least one of them must fail to be n^(1-d)-rich -- i.e. at least one of then meets in the grid in fewer than n^(1-d) points. In this talk I will discuss a closely related result that I and Evan Borenstein have proved, and will perhaps discuss how we think we can use it to polish off this conjecture of Solymosi.

- Series
- Geometry Topology Seminar
- Time
- Monday, September 8, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Roland van der Veen – University of Amsterdam

The hyperbolic volume and the colored Jones polynomial are two of the most powerful invariants in knot theory. In this talk we aim to extend these invariants to arbitrary graphs embedded in 3-space. This provides new tools for studying questions about graph embedding and it also sheds some new light on the volume conjecture. According to this conjecture, the Jones polynomial and the volume of a knot are intimately related. In some special cases we will prove that this still holds true in the case of graphs.

- Series
- CDSNS Colloquium
- Time
- Monday, September 8, 2008 - 16:30 for 2 hours
- Location
- Skiles 269
- Speaker
- Vadim Yu Kaloshin – Mathematics Department, Penn State

Consider the classical Newtonian three-body problem. Call motions oscillatory if as times tends to infinity limsup of maximal distance among the bodies is infinite, while liminf it finite. In the '50s Sitnitkov gave the first rigorous example of oscillatory motions for the so-called restricted three-body problem. Later in the '60s Alexeev extended this example to the three-body. A long-standing conjecture, probably going back to Kolmogorov, is that oscillatory motions have measure zero. We show that for the Sitnitkov example and for the so-called restricted planar circular three-body problem these motions have maximal Hausdorff dimension. This is a joint work with Anton Gorodetski.

- Series
- PDE Seminar
- Time
- Tuesday, September 9, 2008 - 15:15 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Marta Lewicka – School of Mathematics, University of Minnesota

A longstanding problem in the mathematical theory of elasticity is to predict theories of lower-dimensional objects (such as rods, plates or shells), subject to mechanical deformations, starting from the 3d nonlinear theory. For plates, a recent effort (in particular work by Friesecke, James and Muller) has lead to rigorous justification of a hierarchy of such theories (membrane, Kirchhoff, von Karman). For shells, despite extensive use of their ad-hoc generalizations present in the engineering applications, much less is known from the mathematical point of view. In this talk, I will discuss the limiting behaviour (using the notion of Gamma-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d mid-surface S. We prove that the minimizers of the 3d elastic energy converge, after suitable rescaling, to minimizers of a hierarchy of shell models. The limiting functionals (which for plates yield respectively the von Karman, linear, or linearized Kirchhoff theories) are intrinsically linked with the geometry of S. They are defined on the space of infinitesimal isometries of S (which replaces the 'out-of-plane-displacements' of plates), and the space of finite strains (which replaces strains of the `in-plane-displacements'), thus clarifying the effects of rigidity of S on the derived theories. The different limiting theories correspond to different magnitudes of the applied forces, in terms of the shell thickness. This is joint work with M. G. Mora and R. Pakzad.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, September 10, 2008 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Michael Goodisman – School of Biology, Georgia Tech

The evolution of sociality represented one of the major transition points in biological history. Highly social animals such as social insects dominate ecological communities because of their complex cooperative and helping behaviors. We are interested in understanding how evolutionary processes affect social systems and how sociality, in turn, affects the course of evolution. Our research focuses on understanding the social structure and mating biology of social insects. In addition, we are interested in the process of development in the context of sociality. We have found that some social insect females mate with multiple males, and that this behavior affects the structure of colonies. We have also found that colonies adjust their reproductive output in a coordinated and adaptive manner. Finally, we are investigating the molecular basis underlying the striking differences between queens and workers in highly social insects. Overall, our research provides insight into the function and evolutionary success of highly social organisms.

- Series
- Research Horizons Seminar
- Time
- Wednesday, September 10, 2008 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Zhiwu Lin – School of Mathematics, Georgia Tech

A plasma is a gas of ionized particles. For a dilute plasma of very high temperature, the collisions can be ignored. Such situations occur, for example, in nuclear fusion devices and space plasmas. The Vlasov-Poisson and Vlasov-Maxwell equations are kinetic models for such collisionless plasmas. The Vlasov-Poisson equation is also used for galaxy evolution. I will describe some mathematical results on these models, including well-posedness and stability issues.

- Series
- ACO Student Seminar
- Time
- Wednesday, September 10, 2008 - 13:00 for 1 hour (actually 50 minutes)
- Location
- ISyE Executive Classroom
- Speaker
- Joel Sokol – ISyE, Georgia Tech

In order to estimate the spread of potential pandemic diseases and the efficiency of various containment policies, it is helpful to have an accurate model of the structure of human contact networks. The literature contains several explicit and implicit models, but none behave like actual network data with respect to the spread of disease. We discuss the difficulty of modeling real human networks, motivate the study of some open practical questions about network structure, and suggest some possible avenues of attack based on some related research.

- Series
- Stochastics Seminar
- Time
- Thursday, September 11, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Robert Foley – ISyE, Georgia Tech

Under certain conditions, we obtain exact asymptotic expressions for the stationary distribution \pi of a Markov chain. In this talk, we will consider Markov chains on {0,1,...}^2. We are particularly interested in deriving asymptotic expressions when the fluid limit of the most probable paths from the origin to the rare event are nonlinear. For example, we will derive asymptotic expressions for a large deviation along the x-axis (e.g., \pi(\ell, y) for fixed y) when the most probable paths to (\ell,y) initially climb the y-axis before turning southwest and drifting towards (\ell,y).

- Series
- Geometry Topology Working Seminar
- Time
- Friday, September 12, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Stavros Garoufalidis – School of Mathematics, Georgia Tech

We will discuss, with examples, the Jones polynomial of the two simplest knots (the trefoil and the figure eight) and its loop expansion.

- Series
- Combinatorics Seminar
- Time
- Friday, September 12, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Yi Zhao – Georgia State University

Let K^r_{r+1} denote the complete r-graph on r+1 vertices. The Turan density of K^r_{r+1} is the largest number t such that there are infinitely many K^r_{r+1}-free r-graphs with edge density t-o(1). Determining t(K^r_{r+1}) for r > 2 is a famous open problem of Turan. The best upper bound for even r, t(K^r_{r+1})\leq 1-1/r, was given by de Caen and Sidorenko. In a joint work with Linyuan Lu, we slightly improve it. For example, we show that t(K^r_{r+1})\leq 1 - 1/r - 1/(2r^3) for r=4 mod 6. One of our lemmas also leads to an exact result for hypergraphs. Given r > 2, let p be the smallest prime factor of r-1. Every r-graph on n > r(p-1) vertices such that every r+1 vertices contain 0 or r edges must be empty or a complete star.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, September 15, 2008 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Peijun Li – Department of Mathematics, Purdue University

Near-field optics has developed dramatically in recent years due to the possibility of breaking the diffraction limit and obtaining subwavelength resolution. Broadly speaking, near-field optics concerns phenomena involving evanescent electromagnetic waves, to which the super-resolving capability of near-field optics may be attributed. In order to theoretically understand the physical mechanism of this capability, it is desirable to accurately solve the underlying scattering problem in near-field optics. We propose an accurate global model for one of the important experimental modes of near-field optics, photon scanning tunneling microscopy, and develop a coupling of finite element and boundary integral method for its numerical solution. Numerical experiments will be presented to illustrate the effectiveness of the proposed method and to show the features of wave propagation in photon scanning tunneling microscope. The proposed model and developed method have no limitations on optical or geometrical parameters of probe and sample, they can be used for realistic simulations of various near-field microscope configurations.

- Series
- Geometry Topology Seminar
- Time
- Monday, September 15, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Pallavi Dani – Emory University and LSU

The Dehn function of a finitely presented group measures the difficulty in filling loops in the presentation complex of the group. Higher dimensional Dehn functions are a natural generalization: the n-dimensional Dehn function of a group captures the difficulty of filling n-spheres with (n+1)-balls in suitably defined complexes associated with the group. A fundamental question in the area is that of determining which functions arise as Dehn functions. I will give an overview of known results and describe recent progress in the 2-dimensional case. This is joint work with Josh Barnard and Noel Brady.

- Series
- Analysis Seminar
- Time
- Monday, September 15, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Avram Sidi – Technion, Israel Institute of Technology, Haifa

Variable transformations are used to enhance the normally poor performance of trapezoidal rule approximations of finite-range integrals I[f]=\int^1_0f(x)dx. Letting x=\psi(t), where \psi(t) is an increasing function for 0 < t < 1 and \psi(0)=0 and \psi(1)=1, the trapezoidal rule is applied to the transformed integral I[f]=\int^1_0f(\psi(t))\psi'(t)dt. By choosing \psi(t) appropriately, approximations of very high accuracy can be obtained for I[f] via this approach. In this talk, we survey the various transformations that exist in the literature. In view of recent generalizations of the classical Euler-Maclaurin expansion, we show how some of these transformations can be tuned to optimize the numerical results. If time permits, we will also discuss some recent asymptotic expansions for Gauss-Legendre integration rules in the presence of endpoint singularities and show how their performance can be optimized by tuning variable transformations. The variable transformation approach presents a very flexible device that enables one to write his/her own high-accuracy numerical integration code in a simple way without the need to look up tables of abscissas and weights for special Gaussian integration formulas.

- Series
- Research Horizons Seminar
- Time
- Wednesday, September 17, 2008 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Leonid Bunimovich – School of Mathematics, Georgia Tech

Dynamics of spatially extended systems is often described by Lattice Dynamical Systems (LDS). LDS were introduced 25 years ago independently by four physicists from four countries. Sometimes LDS themselves are quite relevant models of real phenomena. Besides, very often discretizations of partial differential equations lead to LDS. LDS consist of local dynamical systems sitting in the nodes of a lattice which interact between themselves. Mathematical studies of LDS started in 1988 and introduced a thermodynamic formalism for these spatially extended dynamical systems. They allowed to give exact definitions of such previously vague phenomena as space-time chaos and coherent structures and prove their existence in LDS. The basic notions and results in this area will be discussed. It is a preparatory talk for the next day colloquium where Dynamical Networks, i.e. the systems with arbitrary graphs of interactions, will be discussed.

- Series
- ACO Student Seminar
- Time
- Wednesday, September 17, 2008 - 13:30 for 1.5 hours (actually 80 minutes)
- Location
- ISyE Executive Classroom
- Speaker
- Dan Steffy – ISyE, Georgia Tech

A successful approach to solving linear programming problems exactly has been to solve the problems with increasing levels of fixed precision, checking the final basis in exact arithmetic and then doing additional simplex pivots if necessary. This work is a computational study comparing different techniques for the core element of our exact computation: solving sparse rational systems of linear equations exactly.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, September 18, 2008 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Leonid Bunimovich – School of Mathematics, Georgia Tech

It has been found about ten years ago that most of the real networks are not random ones in the Erdos-Renyi sense but have different topology (structure of the graph of interactions between the elements of a network). This finding generated a steady flux of papers analyzing structural aspects of networks. However, real networks are rather dynamical ones where the elements (cells, genes, agents, etc) are interacting dynamical systems. Recently a general approach to the studies of dynamical networks with arbitrary topology was developed. This approach is based on a symbolic dynamics and is in a sense similar to the one introduced by Sinai and the speaker for Lattice Dynamical Systems, where the graph of interactions is a lattice. The new approach allows to analyse a combined effect of all three features which characterize a dynamical network (topology, dynamics of elements of the network and interactions between these elements) on its evolution. The networks are of the most general type, e.g. the local systems and interactions need not to be homogeneous, nor restrictions are imposed on a structure of the graph of interactions. Sufficient conditions on stability of dynamical networks are obtained. It is demonstrated that some subnetworks can evolve regularly while the others evolve chaotically. This approach is a very natural one and thus gives a hope that in many other problems (some will be discussed) on dynamical networks a progress could be expected.

- Series
- Graph Theory Seminar
- Time
- Thursday, September 18, 2008 - 12:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Luke Postle – School of Mathematics, Georgia Tech

Given a configuration of pebbles on the vertices of a connected graph G, a pebbling move is defined as the removal of two pebbles from some vertex, and the placement of one of these on an adjacent vertex. A graph is called pebbleable if for each vertex v there is a sequence of pebbling moves so that at least one pebble can be placed on vertex v. The pebbling number of a graph G is the smallest integer k such that G is pebbleable given any configuration of k pebbles on G. We improve on the bound of Bukh by showing that the pebbling number of a graph of diameter 3 on n vertices is at most the floor of 3n/2 + 2, and this bound is best possible. We give an alternative proof that the pebbling number of a graph of diameter 2 on n vertices is at most n + 1. This is joint work with Noah Streib and Carl Yerger.

- Series
- Stochastics Seminar
- Time
- Thursday, September 18, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Jonathan Mattingly – Dept of Math, Duke University

I will discuss some recent (but modest) results showing the existence and slow mixing of a stationary chain of Hamiltonian oscillators subject to a heat bath. Surprisingly, even these simple results require some delicate stochastic averaging. This is joint work with Martin Hairer.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, September 19, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- John Etnyre – School of Mathematics, Georgia Tech

This will be an introduction to Legendrian knots (these are interesting knots that blend topological and geometric concepts) and a powerful invariant of Legendrian knots in R^3 called contact homology. On the first pass this invariant is combinatorial and has a lot of interesting algebraic structure. In a future talk (probably a few weeks from now), I will explain more about the analytic side of the theory as well as deeper algebraic aspects. This talk should be accessible anyone interested in topology and geometry.

- Series
- Combinatorics Seminar
- Time
- Friday, September 19, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Evan Borenstein – School of Mathematics, Georgia Tech

The Balog-Szemeredi-Gowers theorem is a widely used tool in additive combinatorics, and it says, roughly, that if one has a set A such that the sumset A+A is "concentrated on few values," in the sense that these values v each get close to n representations as v = a+b, with a,b in A, then there is a large subset A' of A such that the sumset A'+A' is "small" -- i.e. it has size a small multiple of n. Later, Sudakov, Szemeredi and Vu generalized this result to handle multiple sums A_1 + ... + A_k. In the present talk we will present a refinement of this result of Sudakov, Szemeredi and Vu, where we get better control on the growth of sums A'+...+A'. This is joint work with Ernie Croot.

- Series
- Probability Working Seminar
- Time
- Friday, September 19, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 168
- Speaker
- Sergio Almada – School of Mathematics, Georgia Tech

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, September 22, 2008 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Dongbin Xiu – Division of Applied Math, Purdue University

There has been growing interest in developing numerical methods for stochastic computations. This is motivated by the need to conduct uncertainty quantification in simulations, where uncertainty is ubiquitous and exists in parameter values, initial and boundary conditions, geometry, etc. In order to obtain simulation results with high fidelity, it is imperative to conduct stochastic computations to incorporate uncertainty from the beginning of the simulations. In this talk we review and discuss a class of fast numerical algorithms based on generalized polynomial chaos (gPC) expansion.The methods are highly efficient, compared to other traditional In addition to the forward stochastic problem solvers, we also discuss gPC-based methods for addressing "modeling uncertainty", i.e., deficiency in mathematical models, and solving inverse problems such as parameter estimation. ones, and suitable for stochastic simulations of complex systems.

- Series
- Analysis Seminar
- Time
- Monday, September 22, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Wing Suet Li – School of Mathematics, Georgia Tech

The Horn inequalities give a characterization of eigenvalues of self-adjoint n by n matrices A, B, C with A+B+C=0. The proof requires powerful tools from algebraic geometry. In this talk I will talk about our recent result of these inequalities that are indeed valid for self-adjoint operators of an arbitrary finite factors. Since in this setting there is no readily available machinery from algebraic geometry, we are forced to look for an analysts friendly proof. A (complete) matricial form of our result is known to imply an affirmative answer to the Connes' embedding problem. Geometers in town especially welcome!

- Series
- Geometry Topology Seminar
- Time
- Monday, September 22, 2008 - 14:30 for 2 hours
- Location
- Room 322, Boyd Graduate Studies UGA
- Speaker
- Stavros Garoufalidis – School of Mathematics, Georgia Tech

I will discuss a relation between the HOMFLY polynomial of a knot, its extension for a closed 3-manifold, a special function, the trilogarithm, and zeta(3). Technically, this means that we consider perturbative U(N) Chern-Simons theory around the trivial flat connection, for all N, in an ambient 3-manifold. This is rigorous, and joint with Marcos Marino and Thang Le.

- Series
- Geometry Topology Seminar
- Time
- Monday, September 22, 2008 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Room 322, Boyd Graduate Studies UGA
- Speaker
- Michael Usher – Department of Mathematics, University of Georgia

Based on work of Schwarz and Oh, information coming from a filtration in Hamiltonian Floer homology can be used to construct "spectral invariants" for paths of Hamiltonian diffeomorphisms of symplectic manifolds. I will show how these invariants can be used to provide a unified approach to proving various old and new results in symplectic topology, including the non-degeneracy of the Hofer metric and some of its variants; a sharp version of an inequality between the Hofer-Zehnder capacity and the displacement energy; and a generalization of Gromov's non-squeezing theorem.

- Series
- ACO Student Seminar
- Time
- Tuesday, September 23, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- ISyE executive classroom
- Speaker
- Prasad Tetali – School of Mathematics, Georgia Tech

The notion of a correlation decay, originating in statistical physics, has recently played an important role in yielding deterministic approximation algorithms for various counting problems. I will try to illustrate this technique with two examples: counting matchings in bounded degree graphs, and counting independent sets in certain subclasses of claw-free graphs.

- Series
- PDE Seminar
- Time
- Tuesday, September 23, 2008 - 15:15 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Michael Shearer – Department of Mathematics, North Carolina State University

Granular materials are important in a wide variety of contexts, such as avalanches and industrial processing of powders and grains. In this talk, I discuss some of the issues in understanding how granular materials flow, and especially how they tend to segregate by size. The segregation process, known scientifically as kinetic sieving, and more colorfully as The Brazil Nut Effect, involves the tendency of small particles to fall into spaces created by large particles. The small particles then force the large particles upwards, as in a shaken can of mixed nuts, in which the large Brazil nuts tend to end up near the lid. I'll describe ongoing physics experiments, mathematical modeling of kinetic sieving, and the results of analysis of the models (which are nonlinear partial differential equations). Movies of simulations and exact solutions illustrate the role of shock waves after layers of small and large particles have formed.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, September 24, 2008 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Reinhard Laubenbacher – Virginia Bioinformatics Institute and Department of Mathematics, Virginia Tech

Since John von Neumann introduced cellular automata in the 1950s to study self-replicating systems, algebraic models of different kinds have increased in popularity in network modeling in systems biology. Their common features are that the interactions between network nodes are described by "rules" and that the nodes themselves typically take on only finitely many states, resulting in a time-discrete dynamical system with a finite state space. Some advantages of such qualitative models are that they are typically intuitive, can accommodate noisy data, and require less information about a variety of kinetic and other parameters than differential equations models. Yet they can capture essential network features in many cases. This talk will discuss examples of different types of algebraic models of molecular networks and a common conceptual framework for their analysis.

- Series
- Research Horizons Seminar
- Time
- Wednesday, September 24, 2008 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Jeff Geronimo – School of Mathematics, Georgia Tech

A Turning point is where solutions to differential equations change behavior from exponential to oscillatory. In this region approximate solutions given by the powerful WKB method break down. In a series of paper in the 30's and 40's Langer developed a transformation (the Langer transformation) that allows the development of good approximate solutions (in terms of Airy functions) in the region of the Turning point I will discuss a discrete analog of this transformation and show how it leads to nice asymptotic formulas for various orthogonal polynomials.

- Series
- Combinatorics Seminar
- Time
- Thursday, September 25, 2008 - 12:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Hanno Lefmann – Technical University Chemnitz, Germany

Motivated by a question raised by P\'or and Wood in connection with compact embeddings of graphs into the grid {\mathbb Z}^d, we consider generalizations of the no-three-in-line-problem. For several pairs (d,k,l) we give algorithmic or probabilistic, combinatorial lower, and upper bounds on the largest sizes of subsets S of grid-points in the d-dimensional T \times ... \times T-grid, where T is large and no l distinct grid-points of S are contained in a k-dimensional affine or linear subspace.

- Series
- Stochastics Seminar
- Time
- Thursday, September 25, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Robert Serfling – Department of Mathematical Sciences, University of Texas at Dallas

Robustness of several nonparametric multivariate "threshold type" outlier identification procedures is studied, employing a masking breakdown point criterion subject to a fixed false positive rate. The procedures are based on four different outlyingness functions: the widely-used "Mahalanobis distance" version, a new one based on a "Mahalanobis quantile" function that we introduce, one based on the well-known "halfspace" depth, and one based on the well-known "projection" depth. In this treatment, multivariate location outlyingness functions are formulated as extensions of univariate versions using either "substitution" or "projection pursuit," and an equivalence paradigm relating multivariate depth, outlyingness, quantile, and centered rank functions is applied. Of independent interest, the new "Mahalanobis quantile" outlyingness function is not restricted to have elliptical contours, has a transformation-retransformation representation in terms of the well-known spatial outlyingness function, and corrects to full affine invariance the orthogonal invariance of that function. Here two special tools, also of independent interest, are introduced and applied: a notion of weak covariance functional, and a very general and flexible formulation of affine equivariance for multivariate quantile functions. The new Mahalanobis quantile function inherits attractive features of the spatial version, such as computational ease and a Bahadur-Kiefer representation. For the particular outlyingness functions under consideration, masking breakdown points are evaluated and compared within a contamination model. It is seen that for threshold type outlier identification the Mahalanobis distance and projection procedures are superior to the others, although all four procedures are quite suitable for robust ranking of points with respect to outlyingness. Reasons behind these differences are discussed, and directions for further study are indicated.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, September 26, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Jim Krysiak – School of Mathematics, Georgia Tech

This will be a presentation of the classical result on the existence of three closed nonselfintersecting geodesics on surfaces diffeomorphic to the sphere. It will be accessible to anyone interested in topology and geometry.

- Series
- Probability Working Seminar
- Time
- Friday, September 26, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 168
- Speaker
- Stas Minsker – School of Mathematics, Georgia Tech

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, September 29, 2008 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Silas Alben – School of Mathematics, Georgia Tech

We discuss two problems. First: When a piece of paper is crumpled, sharp folds and creases form. These are distributed over the sheet in a complex yet fascinating pattern. We study experimentally a two-dimensional version of this problem using thin strips of paper confined within rings of shrinking radius. We find a distribution of curvatures which can be fit by a power law. We provide a physical argument for the power law using simple elasticity and geometry. The second problem considers confinement of charged polymers to the surface of a sphere. This is a generalization of the classical Thompson model of the atom and has applications in the confinement of RNA and DNA in viral shells. Using computational results and asymptotics we describe the sequence of configurations of a simple class of charged polymers.

- Series
- Analysis Seminar
- Time
- Monday, September 29, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Wing Suet Li – School of Mathematics, Georgia Tech

The Horn inequalities give a characterization of eigenvalues of self-adjoint n by n matrices A, B, C with A+B+C=0. The proof requires powerful tools from algebraic geometry. In this talk I will talk about our recent result of these inequalities that are indeed valid for self-adjoint operators of an arbitrary finite factors. Since in this setting there is no readily available machinery from algebraic geometry, we are forced to look for an analysts friendly proof. A (complete) matricial form of our result is known to imply an affirmative answer to the Connes' embedding problem. Geometers especially welcome!

- Series
- Geometry Topology Seminar
- Time
- Monday, September 29, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Igor Belegradek – School of Mathematics, Georgia Tech

This is an expository talk. A classical theorem of Mazur gives a simple criterion for two closed manifolds M, M' to become diffeomorphic after multiplying by the Euclidean n-space, where n large. In the talk I shall prove Mazur's theorem, and then discuss what happens when n is small and M, M' are 3-dimensional lens spaces. The talk shall be accessible to anybody with interest in geometry and topology.

- Series
- PDE Seminar
- Time
- Tuesday, September 30, 2008 - 15:15 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Marian Bocea – North Dakota State University, Fargo

The yield set of a polycrystal may be characterized using variational principles associated to suitable supremal functionals. I will describe some model problems for which these can be obtained via Gamma-convergence of a class of "power-law" functionals acting on fields satisfying appropriate differential constraints, and I will indicate some PDEs which play a role in the analysis of these problems.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, October 1, 2008 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- John Drake – UGA

- Series
- Research Horizons Seminar
- Time
- Wednesday, October 1, 2008 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Roland van der Veen – University of Amsterdam

In this introduction to knot theory we will focus on a class of knots called rational knots. Here the word rational refers to a beautiful theorem by J. Conway that sets up a one to one correspondence between these knots and the rational numbers using continued fractions. We aim to give an elementary proof of Conway's theorem and discuss its application to the study of DNA recombination. No knowledge of topology is assumed.

- Series
- ACO Student Seminar
- Time
- Wednesday, October 1, 2008 - 13:30 for 2 hours
- Location
- ISyE Executive Classroom
- Speaker
- Daniel Dadush – ACO, Georgia Tech

Constraint Programming is a powerful technique developed by the Computer Science community to solve combinatorial problems. I will present the model, explain constraint propagation and arc consistency, and give some basic search heuristics. I will also go through some illustrative examples to show the solution process works.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, October 2, 2008 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- John Etnyre – School of Mathematics, Georgia Tech

Describe the trajectories of particles floating in a liquid. This is a surprisingly difficult problem and attempts to understand it have involved many diverse techniques. In the 60's Arold, Marsden, Ebin and others began to introduce topological techniques into the study of fluid flows. In this talk we will discuss some of these ideas and see how they naturally lead to the introduction of contact geometry into the study of fluid flows. We then consider some of the results one can obtain from this contact geometry perspective. For example we will show that for a sufficiently smooth steady ideal fluid flowing in the three sphere there is always some particle whose trajectory is a closed loop that bounds an embedded disk, and that (generically) certain steady Euler flows are (linearly) unstable.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, October 2, 2008 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- John Etnyre – School of Mathematics, Georgia Tech

Describe the trajectories of particles floating in a liquid. This is a surprisingly difficult problem and attempts to understand it have involved many diverse techniques. In the 60's Arold, Marsden, Ebin and others began to introduce topological techniques into the study of fluid flows. In this talk we will discuss some of these ideas and see how they naturally lead to the introduction of contact geometry into the study of fluid flows. We then consider some of the results one can obtain from this contact geometry perspective. For example we will show that for a sufficiently smooth steady ideal fluid flowing in the three sphere there is always some particle whose trajectory is a closed loop that bounds an embedded disk, and that (generically) certain steady Euler flows are (linearly) unstable.

- Series
- Stochastics Seminar
- Time
- Thursday, October 2, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Mark Huber – Departments of Mathematics and Statistical Sciences, Duke University

Spatial data are often more dispersed than would be expected if the points were independently placed. Such data can be modeled with repulsive point processes, where the points appear as if they are repelling one another. Various models have been created to deal with this phenomenon. Matern created three algorithms that generate repulsive processes. Here, MatÃ©rn Type III processes are used to approximate the likelihood and posterior values for data. Perfect simulation methods are used to draw auxiliary variables for each spatial point that are part of the type III process.

- Series
- Geometry Topology Seminar
- Time
- Friday, October 3, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Tony Pantev – Dept of Mathematics, University of Penn

I will describe a framework which relates large N duality to the geometry of degenerating Calabi-Yau spaces and the Hitchin integrable system. I will give a geometric interpretation of the Dijkgraaf-Vafa large N quantization procedure in this context.

- Series
- Combinatorics Seminar
- Time
- Friday, October 3, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Ian Goulden – University of Waterloo

This is an expository account of recent work on the enumeration of maps (graphs embedded on a surface of arbitrary genus) and branched covers of the sphere. These combinatorial and geometric objects can both be represented by permutation factorizations, in the which the subgroup generated by the factors acts transitively on the underlying symbols (these are called "transitive factorizations"). Various results and methods are discussed, including a number of methods from mathematical physics, such as matrix integrals and the KP hierarchy of integrable systems. A notable example of the results is a recent recurrence for triangulations of a surface of arbitrary genus obtained from the simplest partial differential equation in the KP hierarchy. The recurrence is very simple, but we do not know a combinatorial interpretation of it, yet it leads to precise asymptotics for the number of triangulations with n edges, of a surface of genus g.

- Series
- Probability Working Seminar
- Time
- Friday, October 3, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 168
- Speaker
- Christian Houdre – School of Mathematics, Georgia Tech

- Series
- Graph Theory Seminar
- Time
- Monday, October 6, 2008 - 11:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Hein van der Holst – University of Eindhoven

For an undirected graph G=(V,E) with V={1,...,n} let S(G) be the set of all symmetric n x n matrices A=[a_i,j] with a_i,j non-zero for distinct i,j if and only if ij is an edge. The inertia of a symmetric matrix is the triple (p_+,p_-,p_0), where p_+, p_-,p_0 are the number of positive, negative, and null eigenvalues respectively. The inverse inertia problem asks which inertias can be obtained by matrices in S(G). This problem has been studied intensively by Barrett, Hall, and Loewy. In this talk I will present new results on the inverse inertia problem, among them a Colin de Verdiere type invariant for the inertia set (this is the set of all possible inertias) of a graph, a formula for the inertia set of graphs with a 2-separation, and a formula for the inertia set of the join of a collection of graphs.
The Colin de Verdiere type invariant for the inertia set is joint work with F. Barioli, S.M. Fallat, H.T. Hall, D. Hershkowitz, L. Hogben, and B. Shader, and the formula for the inertia set of the join of a collection of graphs is joint work with W. Barrett and H.T. Hall.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, October 6, 2008 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Shengfu Deng – School of Mathematics, Georgia Tech

We consider the three-dimensional gravity-capillary waves on water of finite-depth which are uniformly translating in a horizontal propagating direction and periodic in a transverse direction. The exact Euler equations are formulated as a spatial dynamical system in stead of using Hamiltonian formulation method. A center-manifold reduction technique and a normal form analysis are applied to show that the dynamical system can be reduced to a system of ordinary differential equations. Using the existence of a homoclinic orbit connecting to a two-dimensional periodic solution for the reduced system, it is shown that such a generalized solitary-wave solution persists for the original system by applying a perturbation method and adjusting some appropriate constants.

- Series
- Geometry Topology Seminar
- Time
- Monday, October 6, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- A. Sikora – SUNY Buffalo

W. Goldman proved that the SL(2)-character variety X(F) of a closed surface F is a holonomic symplectic manifold. He also showed that the Sl(2)-characters of every 3-manifold with boundary F form an isotropic subspace of X(F). In fact, for all 3-manifolds whose SL(2)-representations are easy to analyze, these representations form a Lagrangian space. In this talk, we are going to construct explicit examples of 3-manifolds M bounding surfaces of arbitrary genus, whose spaces of SL(2)-characters have dimension as small as possible. We discuss relevance of this problem to quantum and classical low-dimensional topology.

- Series
- Analysis Seminar
- Time
- Monday, October 6, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Hrant Hakobyan – University of Toronto

A mapping F between metric spaces is called quasisymmetric (QS) if for every triple of points it distorts their relative distances in a controlled fashion. This is a natural generalization of conformality from the plane to metric spaces. In recent times much work has been devoted to the classification of metric spaces up to quasisymmetries. One of the main QS invariants of a space X is the conformal dimension, i.e the infimum of the Hausdorff dimensions of all spaces QS isomorphic to X. This invariant is hard to find and there are many classical fractals such as the standard Sierpinski carpet for which conformal dimension is not known. Tyson proved that if a metric space has sufficiently many curves then there is a lower bound for the conformal dimension. We will show that if there are sufficiently many thick Cantor sets in the space then there is a lower bound as well. "Sufficiently many" here is in terms of a modulus of a system of measures due to Fuglede, which is a generalization of the classical conformal modulus of Ahlfors and Beurling. As an application we obtain a new lower bound for the conformal dimension of self affine McMullen carpets.

- Series
- PDE Seminar
- Time
- Tuesday, October 7, 2008 - 15:15 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Nassif Ghoussoub – University of British Columbia, Canada

We describe how several nonlinear PDEs and evolutions including stationary and dynamic Navier-Stokes equations can be formulated and resolved variationally by minimizing energy functionalsof the form
I(u) = L(u, -\Lambda u) + \langle \Lambda u, u\rangle
and
I(u) = \Int^T_0 [L(t, u(t), -\dot u(t) - \Lambda u(t)) + \langle\Lambda u(t), u(t)\rangle]dt + \ell (u(0) - u(T)
\frac{u(T) + u(0)}{2}
where L is a time-dependent "selfdual Lagrangian" on state space, is another selfdual "boundary Lagrangian", and is a nonlinear operator (such as \Lambda u = div(u \otimes u) in the Navier-Stokes case). However, just like the selfdual Yang-Mills equations, the equations are not obtained via Euler-Lagrange theory, but from the fact that a natural infimum is attained. In dimension 2, we recover the well known solutions for the corresponding initial-value problem as well as periodic and anti-periodic ones, while in dimension 3 we get Leray solutions for the initial-value problems, but also solutions satisfying u(0) = \alpha u(T ) for any given in (-1, 1). It is worth noting that our variational principles translate into Leray's energy identity in dimension 2 (resp., inequality in dimension 3). Our approach is quite general and does apply to many other situations.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, October 8, 2008 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Dr. John Glasser – CDC/CCID/NCIRD

**Background:** We endeavor to reproduce historical observations and to identify and remedy the cause of any disparate predictions before using models to inform public policy-making. We have no finely age- and time-stratified observations from historical pandemics, but prior exposure of older adults to a related strain is among the more compelling hypotheses for the w-shaped age-specific mortality characterizing the 1918 pandemic, blurring the distinction between annual and pandemic influenza.

** Methods:** We are attempting to reproduce patterns in annual influenza morbidity and mortality via a cross-classified compartmental model whose age class sojourns approximate the longevity of clusters of closely-related strains. In this population model, we represent effective inter-personal contacts via a generalization of Hethcote's formulation of mixing as a convex combination of contacts within and between age groups. Information about mixing has been sought in face-to-face conversations, a surrogate for contacts by which respiratory diseases might be transmitted, but could also be obtained from household and community transmission studies. We reanalyzed observations from several such studies to learn about age-specific preferences, proportions of contacts with others the same age. And we obtained age-specific forces of infection from proportions reporting illness in a prospective study of household transmission during the 1957 influenza pandemic, which we gamma distributed to correct for misclassification. Then we fit our model to weekly age-specific hospitalizations from Taiwan's National Health Insurance Program, 2000-07, by adjusting a) age-specific coefficients of harmonic functions by which we model seasonality and b) probabilities of hospitalization given influenza.

** Results:** While our model accounts for only 30% of the temporal variation in hospitalizations, estimated conditional probabilities resemble official health resource utilization statistics. Moreover, younger and older people are most likely to be hospitalized and elderly ones to die of influenza, with modeled deaths 10.6% of encoded influenza or pneumonia mortality.

** Conclusions:** Having satisfactorily reproduced recent patterns in influenza morbidity and mortality in Taiwan via a deterministic model, we will switch to a discrete event-time simulator and - possibly with different initial conditions and selected parameters - evaluate the sufficiency of projected pandemic vaccine production.

Joint work with Denis Taneri, and Jen-Hsiang Chuang

- Series
- ACO Student Seminar
- Time
- Wednesday, October 8, 2008 - 13:30 for 2 hours
- Location
- Skiles 269
- Speaker
- Atish Das Sarma – CS/ACO, Georgia Tech

This study focuses on computations on large graphs (e.g., the web-graph) where the edges of the graph are presented as a stream. The objective in the streaming model is to maintain small amount of memory and perform few passes over the data.
In the streaming model, we show how to perform several graph computations including estimating the probability distribution after a random walk of certain length l, estimate the mixing time, and the conductance. We can compute the approximate PageRank values in O(nM^{-1/4}) space and O(M^{3/4}) passes (where n is the number of nodes and M is the mixing time of the graph). In comparison, a standard (matrix-vector multiplication) implementation of the PageRank algorithm will take O(n) space and O(M) passes. The main ingredient in all our algorithms is to explicitly perform several random walks of certain length efficiently in the streaming model. I shall define and motivate the streaming model and the notion of PageRank, and describe our results and techniques.
Joint work with Sreenivas Gollapudi and Rina Panigrahy from Microsoft Research.

- Series
- Graph Theory Seminar
- Time
- Thursday, October 9, 2008 - 12:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Roland van der Veen – University of Amsterdam

The aim of this talk is to introduce techniques from knot theory into the study of graphs embedded in 3-space. The main characters are hyperbolic geometry and the Jones polynomial. Both have proven to be very successful in studying knots and conjecturally they are intimately related. We show how to extend these techniques to graphs and discuss possible applications. No prior knowledge of knot theory or geometry will be assumed.

- Series
- Combinatorics Seminar
- Time
- Thursday, October 9, 2008 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Lincoln Lu – University of South Carolina

We consider a random subgraph G_p of a host graph G formed by retaining each edge of G with probability p. We address the question of determining the critical value p (as a function of G) for which a giant component emerges. Suppose G satisfies some (mild) conditions depending on its spectral gap and higher moments of its degree sequence. We define the second order average degree \tilde{d} to be \tilde{d}=\sum_v d_v^2/(\sum_v d_v) where d_v denotes the degree of v. We prove that for any \epsilon > 0, if p > (1+ \epsilon)/\tilde{d} then almost surely the percolated subgraph G_p has a giant component. In the other direction, if p < (1-\epsilon)/\tilde{d} then almost surely the percolated subgraph G_p contains no giant component. (Joint work with Fan Chung Graham and Paul Horn)

- Series
- Geometry Topology Seminar
- Time
- Friday, October 10, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Vera Vertesi – School of Mathematics, Georgia Tech

In this talk I will give a purely combinatorial description of Knot Floer Homology for knots in the three-sphere (Manolescu-Ozsvath-Szabo- Thurston). In this homology there is a naturally associated invariant for transverse knots. This invariant gives a combinatorial but still an effective way to distinguish transverse knots (Ng-Ozsvath-Thurston). Moreover it leads to the construction of an infinite family of non-transversely simple knot-types (Vertesi).

- Series
- Probability Working Seminar
- Time
- Friday, October 10, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 168
- Speaker
- Stas Minsker – School of Mathematics, Georgia Tech

Based on a paper by E. Candes and Y. Plan.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, October 15, 2008 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Yang Kuang – Arizona State University

Chronic HBV infection affects 350 million people and can lead to death through cirrhosis-induced liver failure or hepatocellular carcinoma. We present the rich dynamics of two recent models of HBV infection with logistic hepatocyte growth and a standard incidence function governing viral infection. One of these models also incorporates an explicit time delay in virus production. All model parameters can be estimated from biological data. We simulate a course of lamivudine therapy and find that the models give good agreement with clinical data. Previous models considering constant hepatocyte growth have permitted only two dynamical possibilities: convergence to a virus free or an endemic steady state. Our models admit periodic solutions. Minimum hepatocyte populations are very small in the periodic orbit, and such a state likely represents acute liver failure. Therefore, the often sudden onset of liver failure in chronic HBV patients can be explained as a switch in stability caused by the gradual evolution of parameters representing the disease state.

- Series
- Research Horizons Seminar
- Time
- Wednesday, October 15, 2008 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Ben Webb – School of Mathematics, Georgia Tech

In the study of one dimensional dynamical systems it is often assumed that the functions involved have a negative Schwarzian derivative. However, as not all one dimensional systems of interest have this property it is natural to consider a generalization of this condition. Specifically, we consider the interval functions of a real variable having some iterate with a negative Schwarzian derivative and show that many known results generalize to this larger class, that is to functions with an eventual negative Schwarzian derivative. The property of having an eventual negative Schwarzian derivative is nonasymptotic therefore verification of whether a function has such an iterate can often be done by direct computation. The introduction of this class was motivated by some maps arising in neuroscience.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, October 16, 2008 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Mohammad Ghomi – School of Mathematics, Georgia Tech

We prove that a smooth compact submanifold of codimension $2$ immersed in $R^n$, $n>2$, bounds at most finitely many topologically distinct compact nonnegatively curved hypersurfaces. This settles a question of Guan and Spruck related to a problem of Yau. Analogous results for complete fillings of arbitrary Riemannian submanifolds are obtained as well. On the other hand, we show that these finiteness theorems may not hold if the codimension is too high, or the prescribed boundary is not sufficiently regular. Our proofs employ, among other methods, a relative version of Nash's isometric embedding theorem, and the theory of Alexandrov spaces with curvature bounded below, including the compactness and stability theorems of Gromov and Perelman. These results consist of joint works with Stephanie Alexander and Jeremy Wong, and Robert Greene.

- Series
- Stochastics Seminar
- Time
- Thursday, October 16, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Tony Cai – Department of Statistics, The Wharton School, University of Pennsylvania

Adaptive estimation of linear functionals occupies an important position in the theory of nonparametric function estimation. In this talk I will discuss an adaptation theory for estimation as well as for the construction of confidence intervals for linear functionals. A between class modulus of continuity, a geometric quantity, is shown to be instrumental in characterizing the degree of adaptability and in the construction of adaptive procedures in the same way that the usual modulus of continuity captures the minimax difficulty of estimation over a single parameter space. Our results thus "geometrize" the degree of adaptability.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, October 17, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Jim Krysiak – School of Mathematics, Georgia Tech

This will be a continuation of the previous talk by this title. Specifically, this will be a presentation of the classical result on the existence of three closed nonselfintersecting geodesics on surfaces diffeomorphic to the sphere. It will be accessible to anyone interested in topology and geometry.

- Series
- Combinatorics Seminar
- Time
- Friday, October 17, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Ravi Montenegro – University of Massachussetts

The Birthday Paradox says that if there are N days in a year, and 1.2*sqrt(N) days are chose uniformly at random with replacement, then there is a 50% probability that some day was chosen twice. This can be interpreted as a statement about self-intersection of random paths of length 1.2*sqrt(N) on the complete graph K_N with loops. We prove an extension which shows that for many graphs random paths with length of order sqrt(N) will have the same self-intersection property. We finish by discussing an application to the Pollard Rho Algorithm for Discrete Logarithm. (joint work with Jeong-Han Kim, Yuval Peres and Prasad Tetali).

- Series
- Combinatorics Seminar
- Time
- Monday, October 20, 2008 - 11:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Chris Godsil – University of Waterloo

In its simplest form, the Erdos-Ko-Rado theorem tells us that if we have a family F of subsets of size k from set of size v such that any two sets in the family have at least one point in common, then |F|<=(v-1)\choose(k-1) and, if equality holds, then F consists of all k-subsets that contain a given element of the underlying set.
This theorem can also be viewed as a result in graph theory, and from this viewpoint it has many generalizations. I will outline how it can be proved using linear algebra, and then discuss how this approach can be applied in other cases.

- Series
- Geometry Topology Seminar
- Time
- Monday, October 20, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Iain Moffatt – University of Southern Alabama

In this talk I will describe some relations between embedded graphs, their polynomials and the Jones polynomial of an associated link. I will explain how relations between graphs, links and their polynomials leads to the definition of the partial dual of a ribbon graph. I will then go on to show that the realizations of the Jones polynomial as the Tutte polynomial of a graph, and as the topological Tutte polynomial of a ribbon graph are related, surprisingly, by the homfly polynomial.

- Series
- Other Talks
- Time
- Tuesday, October 21, 2008 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Klaus Building, 1116E&amp;W
- Speaker
- Leslie Valiant – Division of Engineering and Applied Sciences, Harvard University

We argue that computational models have an essential role in uncovering the principles behind a variety of biological phenomena that cannot be approached by other means. In this talk we shall focus on evolution. Living organisms function according to complex mechanisms that operate in different ways depending on conditions. Darwin's theory of evolution suggests that such mechanisms evolved through random variation guided by natural selection. However, there has existed no theory that would explain quantitatively which mechanisms can so evolve in realistic population sizes within realistic time periods, and which are too complex. Here we suggest such a theory. Evolution is treated as a form of computational learning from examples in which the course of learning depends only on the aggregate fitness of the current hypothesis on the examples, and not otherwise on individual examples. We formulate a notion of evolvability that distinguishes function classes that are evolvable with polynomially bounded resources from those that are not. For example, we can show that monotone Boolean conjunctions and disjunctions are demonstrably evolvable over the uniform distribution, while Boolean parity functions are demonstrably not. We shall discuss some broader issues in evolution and intelligence that can be addressed via such an approach.

- Series
- Research Horizons Seminar
- Time
- Tuesday, October 21, 2008 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Selma Yildirim – School of Mathematics, Georgia Tech

We consider the pseudodifferential operators H_{m,\Omega} associated by the prescriptions of quantum mechanics to the Klein-Gordon Hamiltonian when restricted to a compact domain \Omega in {\mathbb R}^d. When the mass m is 0 the operator H_{0,\Omega} coincides with the generator of the Cauchy stochastic process with a killing condition on \partial \Omega. (The operator H_{0,\Omega} is sometimes called the fractional Laplacian with power 1/2.) We prove several universal inequalities for the eigenvalues (joint work with Evans Harrell).

- Series
- ACO Seminar
- Time
- Tuesday, October 21, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Stephan Held – University of Bonn

A central characteristic of a computer chip is the speed at which it processes data, determined by the time it takes electrical signals to travel through the chip. A major challenge in the design of a chip is to achieve timing closure, that is to find a physical realization fulfilling the speed specifications. We give an overview over the major tasks for optimizing the performance of computer chips and present several new algorithms. For the topology generation of repeater trees, we introduce a variant of the Steiner tree problem and present fast algorithm that balances efficiently between the resource consumption and performance. Another indispensable task is gate sizing, a discrete optimization problem with nonlinear or PDE constraints, for which a fast heuristic is introduced. The effectiveness in practice is demonstrated by comparing with newly developed lower bounds for the achievable delay. We conclude with a variant of the time-cost tradeoff problem from project management. In contrast to the usual formulation cycles are allowed. We present a new method to compute the time-cost tradeoff curve in such instances using combinatorial algorithms. Several problems in chip design can be modeled as time-cost tradeoff problems, e.g. threshold voltage optimization of plane assignment.

- Series
- PDE Seminar
- Time
- Tuesday, October 21, 2008 - 15:15 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Sigurd Angenent – University of Wisconsin, Madison

I will discuss a few ways in which reaction diffusion models have been used to pattern formation. In particular in the setting of Cdc42 transport to and from the membrane in a yeast cell I will show a simple model which achieves polarization. The model and its analysis exhibits some striking differences between deterministic and probabilistic versions of the model.

- Series
- Joint School of Mathematics and ACO Colloquium
- Time
- Tuesday, October 21, 2008 - 16:30 for 2 hours
- Location
- Skiles 255
- Speaker
- Chris Godsil – University of Waterloo

Refreshments will be served at 4PM in Skiles 236.

The possibility of a quantum computer has lead to much new work in theoretical physics and, naturally enough, this work has raised many new mathematical problems. What is perhaps surprising is that it has lead to interesting problems in algebraic graph theory. For example, questions about the relative power of quantum computer and classical computers lead to questions about the chromatic number of certain graphs. In my talk I will discuss some of these problems, and the progress that has been made.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Wednesday, October 22, 2008 - 10:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Arthur Szlam – UCLA

SPECIAL TIME AND LOCATION FOR THIS WEEK ONLY

The k-planes method is the generalization of k-means where the representatives of each cluster are affine linear sets. In this talk I will describe some possible modifications of this method for discriminative learning problems.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, October 22, 2008 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Andy Bommarius – School of Chemistry &amp; Biochemistry, Georgia Tech

After rational protein design and combinatorial protein engineering (directed evolution), data-driven protein engineering emerges as a third generation of techniques for improving protein properties. Data-driven protein engineering relies heavily on the use of mathematical algorithms. In the first example, we developed a method for predicting the positions in the amino acid sequence that are critical for the catalytic activity of a protein. With nucleotide sequences of both functional and non-functional variants and a Support Vector Machine (SVM) learning algorithm, we set out to narrow the interesting sequence space of proteins, i.e. find the truly relevant positions. Variants of TEM-1 β-lactamase were created in silico using simulations of both mutagenesis and recombination protocols. The algorithm was shown to be able to predict critical positions that can tolerate up to two amino acids. Pairs of amino acid residues are known to lead to inactive sequences, unless mutated jointly. In the second example, we combine SVM, Boolean learning (BL), and the combination of the two, BLSVM, to find such interactive residues. Results on interactive residues in two fluorescent proteins, Discosoma Red Fluorescent Protein (Ds-Red) and monomeric Red Fluorescent Protein (mRFP), will be presented.

- Series
- Mathematical Finance/Financial Engineering Seminar
- Time
- Wednesday, October 22, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- ZhengJun Zhang – University of Wisconsin

Various correlation measures have been introduced in statistical inferences and applications. Each of them may be used in measuring association strength of the relationship, or testing independence, between two random variables. The quotient correlation is defined here as an alternative to Pearson's correlation that is more intuitive and flexible in cases where the tail behavior of data is important. It measures nonlinear dependence where the regular correlation coefficient is generally not applicable. One of its most useful features is a test statistic that has high power when testing nonlinear dependence in cases where the Fisher's Z-transformation test may fail to reach a right conclusion. Unlike most asymptotic test statistics, which are either normal or \chi 2, this test statistic has a limiting gamma distribution (henceforth the gamma test statistic). More than the common usages of correlation, the quotient correlation can easily and intuitively be adjusted to values at tails. This adjustment generates two new concepts -- the tail quotient correlation and the tail independence test statistics, which are also gamma statistics. Due to the fact that there is no analogue of the correlation coefficient in extreme value theory, and there does not exist an efficient tail independence test statistic, these two new concepts may open up a new field of study. In addition, an alternative to Spearman's rank correlation: a rank based quotient correlation is also defined. The advantages of using these new concepts are illustrated with simulated data, and real data analysis of internet traffic, tobacco markets, financial markets...

- Series
- Graph Theory Seminar
- Time
- Thursday, October 23, 2008 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Tom Bohman – CMU

In this lecture I will introduce the method and sketch some recent applications. The main idea is to exploit a natural connection between the evolution of discrete random processes and continuous functions on the real numbers. Roughly speaking, the method is as follows: Given a discrete random process, we calculate the expected change in the random variable (or variables) of interest in one step of the process, write a differential equation suggested by the expected change, and show that the evolution of the random variable over the course of the process is sharply concentrated around the trajectory given by the solution of the differential equation. This allows us to translate simple facts (often combinatorial in nature) about expected changes in one step of the process into strong statements about sharp concentration of the random variable over the entire course of the process.

- Series
- Geometry Topology Seminar
- Time
- Friday, October 24, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Rafal Komendarczyk – University of Pennsylvania

In many physical situations we are interested in topological lower bounds for L^2-energy of volume preserving vector fields. Such situations include for instance evolution of a magnetic field in ideal magnetohydrodynamics. Classical energy bounds involve topological invariants like helicity which measure linkage of orbits in the flow. In this talk I will present a new lower bound in terms of the third order helicity, which is an invariant measuring a third order linkage of orbits. I will also discuss how the third order helicity can be derived from the Milnor's \mu-bar invariant for 3-component links.

- Series
- Combinatorics Seminar
- Time
- Friday, October 24, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Tom Bohman – CMU

Consider the following random graph process. We begin with the empty graph on n vertices and add edges chosen at random one at a time. Each edge is chosen uniformly at random from the collection of pairs of vertices that do not form triangles when added as edges to the existing graph. In this talk I discuss an analysis of the triangle-free process using the so-called differential equations method for random graph processes. It turns out that with high probability the triangle-free process produces a Ramsey R(3,t) graph, a triangle-free graph whose independence number is within a multiplicative constant factor of the smallest possible.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, October 27, 2008 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- George Biros – CSE, Georgia Tech

Fluid membranes are area-preserving interfaces that resist bending. They are models of cell membranes, intracellular organelles, and viral particles. We are interested in developing simulation tools for dilute suspensions of deformable vesicles. These tools should be computationally efficient, that is, they should scale well as the number of vesicles increases. For very low Reynolds numbers, as it is often the case in mesoscopic length scales, the Stokes approximation can be used for the background fluid. We use a boundary integral formulation for the fluid that results in a set of nonlinear integro-differential equations for the vesicle dynamics. The motion of the vesicles is determined by balancing the nonlocal hydrodynamic forces with the elastic forces due to bending and tension. Numerical simulations of such vesicle motions are quite challenging. On one hand, explicit time-stepping schemes suffer from a severe stability constraint due to the stiffness related to high-order spatial derivatives and a milder constraint due to a transport-like stability condition. On the other hand, an implicit scheme can be expensive because it requires the solution of a set of nonlinear equations at each time step. We present two semi-implicit schemes that circumvent the severe stability constraints on the time step and whose computational cost per time step is comparable to that of an explicit scheme. We discretize the equations by using a spectral method in space, and a multistep third-order accurate scheme in time. We use the fast multipole method to efficiently compute vesicle-vesicle interaction forces in a suspension with a large number of vesicles. We report results from numerical experiments that demonstrate the convergence and algorithmic complexity properties of our scheme. Joint work with: Shravan K. Veerapaneni, Denis Gueyffier, and Denis Zorin.

- Series
- Geometry Topology Seminar
- Time
- Monday, October 27, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Mohammad Ghomi – School of Mathematics, Georgia Tech

We prove that every metric of constant curvature on a compact 2-manifold M with boundary bdM induces (at least) four vertices, i.e., local extrema of geodesic curvature, on bdM, if, and only if, M is simply connected. Indeed, when M is not simply connected, we construct hyperbolic, parabolic, and elliptic metrics of constant curvature on M which induce only two vertices on bdM. Furthermore, we characterize the sphere as the only closed orientable Riemannian 2-manifold M which has the four-vertex-property, i.e., the boundary of every compact surface immersed in M has 4 vertices.

- Series
- Analysis Seminar
- Time
- Monday, October 27, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Brett Wick – University of South Carolina

The Dirichlet space is the set of analytic functions on the disc that have a square integrable derivative. In this talk we will discuss necessary and sufficient conditions in order to have a bilinear form on the Dirichlet space be bounded. This condition will be expressed in terms of a Carleson measure condition for the Dirichlet space. One can view this result as the Dirichlet space analogue of Nehari's Theorem for the classical Hardy space on the disc. This talk is based on joint work with N. Arcozzi, R. Rochberg, and E. Sawyer

- Series
- Research Horizons Seminar
- Time
- Wednesday, October 29, 2008 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Christian Houdré – School of Mathematics, Georgia Tech

This talk is not an appetizer to pizza, but rather an appetizer to the main course: Hua Xu's and Trevis Litherland's thesis defenses which will respectively take place on Thursday the 30th of October and November the 6th, in Skiles 269, at 3pm. I will present the history and origins of the problems they have been tackling ("Ulam's problems"). Various interactions with other fields such as Analysis, Algebra (Young Tableaux) or Bioinformatics (Sequence Comparison) will be touched upon. Then, some elementary but rather useful probabilistic techniques will also be introduced and shown how to be applied.

- Series
- Mathematical Finance/Financial Engineering Seminar
- Time
- Wednesday, October 29, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Lily Wang – Department of Statistics, University of Georgia

We analyze a class of semiparametric ARCH models that nests the simple GARCH(1,1) model but has flexible news impact function. A simple estimation method is proposed based on profiled polynomial spline smoothing. Under regular conditions, the proposed estimator of the dynamic coeffcient is shown to be root-n consistent and asymptotically normal. A fast and efficient algorithm based on fast fourier transform (FFT) has been developed to analyze volatility functions with infinitely many lagged variables within seconds. We compare the performance of our method with the commonly used GARCH(1, 1) model, the GJR model and the method in Linton and Mammen (2005) through simulated data and various interesting time series. For the S&P 500 index returns, we find further statistical evidence of the nonlinear and asymmetric news impact functions.

- Series
- Graph Theory Seminar
- Time
- Thursday, October 30, 2008 - 11:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Stavros Garoufalidis – School of Mathematics, Georgia Tech

PLEASE NOTE UNUSUAL TIME

We will consider the problem of counting the number T(n,g) of cubic graphs with n edges on a surface of of genus g, and review was is known in the combinatorial community in the past 30 years, what was conjectured in physics 20 years ago, and what was proven last month in joint work with Thang Le and Marcos Marino, using the Riemann-Hilbert analysis of the Painleve equation. No knowledge of physics or analysis is required.

- Series
- Stochastics Seminar
- Time
- Thursday, October 30, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Hua Xu – School of Mathematics, Georgia Tech

In this presentation, interactions between spectra of classical Gaussian ensembles and subsequence problems are studied with the help of the powerful machinery of Young tableaux. For the random word problem, from an ordered finite alphabet, the shape of the associated Young tableaux is shown to converge to the spectrum of the (generalized) traceless GUE. Various properties of the (generalized) traceless GUE are established, such as a law of large number for the extreme eigenvalues and the convergence of the spectral measure towards the semicircle law. The limiting shape of the whole tableau is also obtained as a Brownian functional. The Poissonized word problem is finally talked, and, with it, the convergence of the whole Poissonized tableaux is derived.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, October 31, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Sinem Celik Onaran – School of Mathematics, Georgia Tech

It is still not known whether every genus g Lefschetz fibration over the 2-sphere admits a section or not. In this talk, we will give a brief background information on Lefschetz fibrations and talk about sections of genus two Lefschetz fibration. We will observe that any holomorphic genus two Lefschetz fibration without seperating singular fibers admits a section. This talk is accessible to anyone interested in topology and geometry.

- Series
- Stochastics Seminar
- Time
- Friday, October 31, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Valentin Konakov – CEMI RAS, Moscow and UNCC, Charlotte

Consider a class of multidimensional degenerate diffusion processes of the following form

X_t = x+\int_0^t (X_s) ds+\int_0^t \sigma(X_s) dW_s,

Y_t = y+\int_0^t F(X_s)ds,

where b,\sigma, F are assumed to be smooth and b,\sigma bounded. Suppose now that \sigma\sigma^* is uniformly elliptic and that \nabla F does not degenerate. These assumptions guarantee that only one Poisson bracket is needed to span the whole space. We obtain a parametrix representation of Mc Kean-Singer type for the density of (X_t,Y_t) from which we derive some explicit Gaussian controls that characterize the additional singularity induced by the degeneracy. This particular representation then allows to give a local limit theorem with the usual convergence rate for an associated Markov chain approximation. The "weak" degeneracy allows to use the local limit Theorem in Gaussian regime but also induces some difficulty to define the suitable approximating process. In particular two time scales appear. Another difficulty w.r.t. the standard literature on the topic, see e.g. Konakov and Mammen (2000), is the unboundedness of F.

- Series
- Combinatorics Seminar
- Time
- Friday, October 31, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Neil Lyall – University of Georgia

We will discuss some extensions/generalizations of the striking and elegant fact (proved independently by Furstenberg and Sarkozy) that any subset of the integers of positive upper density necessarily contains two distinct elements whose difference is a perfect square. This is joint work with Akos Magyar.

- Series
- Dissertation Defense
- Time
- Monday, November 3, 2008 - 13:30 for 2 hours
- Location
- Skiles 114
- Speaker
- Alex Yurchenko – School of Mathematics, Georgia Tech

The first part of this work deals with open dynamical systems. A natural question of how the survival probability depends upon a position of a hole was seemingly never addresses in the theory of open dynamical systems. We found that this dependency could be very essential. The main results are related to the holes with equal sizes (measure) in the phase space of strongly chaotic maps. Take in each hole a periodic point of minimal period. Then the faster escape occurs through the hole where this minimal period assumes its maximal value. The results are valid for all finite times (starting with the minimal period), which is unusual in dynamical systems theory where typically statements are asymptotic when time tends to infinity. It seems obvious that the bigger the hole is the bigger is the escape through that hole. Our results demonstrate that generally it is not true, and that specific features of the dynamics may play a role comparable to the size of the hole.
In the second part we consider some classes of cellular automata called Deterministic Walks in Random Environments on \mathbb Z^1. At first we deal with the system with constant rigidity and Markovian distribution of scatterers on \mathbb Z^1. It is shown that these systems have essentially the same properties as DWRE on \mathbb Z^1 with constant rigidity and independently distributed scatterers. Lastly, we consider a system with non-constant rigidity (so called process of aging) and independent distribution of scatterers. Asymptotic laws for the dynamics of perturbations propagating in such environments with aging are obtained.

- Series
- Analysis Seminar
- Time
- Monday, November 3, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Shannon Bishop – School of Mathematics, Georgia Tech

Pseudodifferential operators and affine pseudodifferential operators arise naturally in the study of wireless communications. We discuss the origins of these operators and give new conditions on the kernels and symbols of pseudodifferential and affine pseudodifferential operators which ensure the operators are trace class (and more generally, Schatten p-class).

- Series
- Research Horizons Seminar
- Time
- Tuesday, November 4, 2008 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Doron Lubinsky – School of Mathematics, Georgia Tech

Orthogonal polynomials play a role in myriads of problems ranging from approximation theory to random matrices and signal processing. Generalizations of orthogonal polynomials - such as biorthogonal polynomials, cardinal series, Muntz polynomials, are used for example, in number theory and numerical analysis. We discuss some of these, and some potential research projects involving them.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, November 5, 2008 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Melissa Kemp – Dept of Biomedical Engineering, Georgia Tech

Hydrogen peroxide has been long considered a harmful reactive oxygen species, but is increasingly appreciated as a cellular signaling molecule. The mechanism by which the cell buffers against intracellular H2O2 accumulation during periods of oxidative stress is not fully understood. I will introduce a detailed network model of the known redox reactions and cellular thiol modifications involved in H2O2 buffering. The model includes anti-oxidative contributions of catalase, glutathione peroxidase, peroxiredoxin, and glutaredoxin, in addition to the cytoplasmic redox buffers, thioredoxin and glutathione. Based on ordinary differential equations, the model utilizes mass action kinetics to describe changes in concentration and redox state of cytoplasmic proteins upon exposure to physiologically relevant concentrations of extracellular H2O2. Simulations match experimental observations of a rapid and transient oxidation of thioredoxin upon exposure to extracellular peroxide. The increase in the concentration of oxidized proteins predicted by the model is simultaneously accompanied by an increase in protein S-glutathionylation, possibly regulating signal transduction in cells undergoing oxidative stress. Ultimately, this network analysis will provide insight into how to target antioxidant therapies for enhanced buffering without impacting the necessary protein oxidation used by cells for signaling purposes.

- Series
- ACO Student Seminar
- Time
- Wednesday, November 5, 2008 - 13:30 for 2 hours
- Location
- ISyE Executive Classroom
- Speaker
- Leonid Bunimovich – School of Mathematics, Georgia Tech

It has been found about ten years ago that most of the real networks are not random ones in the Erdos-Renyi sense but have different topology (structure of the graph of interactions between the elements of a network). This finding generated a steady flux of papers analyzing structural aspects of networks. However, real networks are rather dynamical ones where the elements (cells, genes, agents, etc) are interacting dynamical systems. Recently a general approach to the studies of dynamical networks with arbitrary topology was developed. This approach is based on a symbolic dynamics and is in a sense similar to the one introduced by Sinai and the speaker for Lattice Dynamical Systems, where the graph of interactions is a lattice. The new approach allows to analyze a combined effect of all three features which characterize a dynamical network ( topology, dynamics of elements of the network and interactions between these elements) on its evolution. The networks are of the most general type, e.g. the local systems and interactions need not to be homogeneous, nor restrictions are imposed on a structure of the graph of interactions. Sufficient conditions on stability of dynamical networks are obtained. It is demonstrated that some subnetworks can evolve regularly while the others evolve chaotically. Some natural graph theoretical and dynamical questions appear in the farther developments of this approach. No preliminary knowledge of anything besides basic calculus and linear algebra is required to understand what is going on.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, November 6, 2008 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Chongchun Zeng – School of Mathematics, Georgia Tech

In this talk, we discuss 1.) the nonlinear instability and unstable manifolds of steady solutions of the Euler equation with fixed domains and 2.) the evolution of free (inviscid) fluid surfaces, which may involve vorticity, gravity, surface tension, or magnetic fields. These problems can be formulated in a Lagrangian formulation on infinite dimensional manifolds of volume preserving diffeomorphisms with an invariant Lie group action. In this setting, the physical pressure turns out to come from the combination of the gravity, surface tension, and the Lagrangian multiplier. The vorticity is naturally related to an invariant group action. In the absence of surface tension, the well-known Rayleigh-Taylor and Kelvin-Helmholtz instabilities appear naturally related to the signs of the curvatures of those infinite dimensional manifolds. Based on these considerations, we obtain 1.) the existence of unstable manifolds and L^2 nonlinear instability in the cases of the fixed domains and 2.) in the free boundary cases, the local well-posedness with surface tension in a rather uniform energy method. In particular, for the cases without surface tension which do not involve hydrodynamical instabilities, we obtain the local existence of solutions by taking the vanishing surface tension limit.

- Series
- Stochastics Seminar
- Time
- Thursday, November 6, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Trevis Litherland – School of Mathematics, Georgia Tech

The limiting law of the length of the longest increasing subsequence, LI_n, for sequences (words) of length n arising from iid letters drawn from finite, ordered alphabets is studied using a straightforward Brownian functional approach. Building on the insights gained in both the uniform and non-uniform iid cases, this approach is then applied to iid countable alphabets. Some partial results associated with the extension to independent, growing alphabets are also given. Returning again to the finite setting, and keeping with the same Brownian formalism, a generalization is then made to words arising from irreducible, aperiodic, time-homogeneous Markov chains on a finite, ordered alphabet. At the same time, the probabilistic object, LI_n, is simultaneously generalized to the shape of the associated Young tableau given by the well-known RSK-correspondence. Our results on this limiting shape describe, in detail, precisely when the limiting shape of the Young tableau is (up to scaling) that of the iid case, thereby answering a conjecture of Kuperberg. These results are based heavily on an analysis of the covariance structure of an m-dimensional Brownian motion and the precise form of the Brownian functionals. Finally, in both the iid and more general Markovian cases, connections to the limiting laws of the spectrum of certain random matrices associated with the Gaussian Unitary Ensemble (GUE) are explored.

- Series
- Geometry Topology Seminar
- Time
- Friday, November 7, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Igor Belegradek – School of Mathematics, Georgia Tech

In the 1980s Gromov showed that curvature (in the triangle comparison sense) decreases under branched covers. In this expository talk I shall prove Gromov's result, and then discuss its generalization (due to Allcock) that helps show that some moduli spaces arising in algebraic geometry have contractible universal covers. The talk should be accessible to those interested in geometry/topology.

- Series
- Combinatorics Seminar
- Time
- Friday, November 7, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Asaf Shapira – School of Mathematics, Georgia Tech

Given a set of linear equations Mx=b, we say that a set of integers S is (M,b)-free if it contains no solution to this system of equations. Motivated by questions related to testing linear-invariant Boolean functions, as well as recent investigations in additive number theory, the following conjecture was raised (implicitly) by Green and by Bhattacharyya, Chen, Sudan and Xie: we say that a set of integers S \subseteq [n], is \epsilon-far from being (M,b)-free if one needs to remove at least \epsilon n elements from S in order to make it (M,b)-free. The conjecture was that for any system of homogeneous linear equations Mx=0 and for any \epsilon > 0 there is a *constant* time algorithm that can distinguish with high probability between sets of integers that are (M,0)-free from sets that are \epsilon-far from being (M,0)-free. Or in other words, that for any M there is an efficient testing algorithm for the property of being (M,0)-free. In this paper we confirm the above conjecture by showing that such a testing algorithm exists even for non-homogeneous linear equations. As opposed to most results on testing Boolean functions, which rely on algebraic and analytic arguments, our proof relies on results from extremal hypergraph theory, such as the recent removal lemmas of Gowers, R\"odl et al. and Austin and Tao.

- Series
- Probability Working Seminar
- Time
- Friday, November 7, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 168
- Speaker
- Yuri Bakhtin – School of Mathematics, Georgia Tech

A discrete infinite volume limit for random trees will be constructed and studied.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, November 10, 2008 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Guowei Wei – Michigan State University – weig@msu.edu

Solvation process is of fundamental importance to other complex biological processes, such signal transduction, gene regulation, etc. Solvation models can be roughly divided into two classes: explicit solvent models that treat the solvent in molecular or atomic detail while implicit solvent models take a multiscale approach that generally replaces the explicit solvent with a dielectric continuum. Because of their fewer degrees of freedom, implicit solvent methods have become popular for many applications in molecular simulation with applications in the calculations of biomolecular titration states, folding energies, binding affinities, mutational effects, surface properties, and many other problems in chemical and biomedical research. In this talk, we introduce a geometric flow based multiscale solvation model that marries a microscopic discrete description of biomolecules with a macroscopic continuum treatment of the solvent. The free energy functional is minimized by coupled geometric and potential flows. The geometric flow is driven not only by intrinsic forces, such as mean curvatures, but also by extrinsic potential forces, such as those from electrostatic potentials. The potential flow is driven mainly by a Poisson-Boltzmann like operator. Efficient computational methods, namely the matched interface and boundary (MIB) method, is developed for to solve the Poisson- Boltzmann equation with discontinuous interface. A Dirichlet- to-Neumann mapping (DTN) approach is developed to regularize singular charges from biomolecules.

- Series
- Analysis Seminar
- Time
- Monday, November 10, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Stavros Garoufalidis – School of Mathematics, Georgia Tech

It is easy to ask for the number T(g,n) of (rooted) graphs with n edges on a surface of genus g. Bender et al gave an asymptotic expansion for fixed g and large n. The contant t_g remained missing for over 20 years, although it satisfied a complicated nonlinear recursion relation. The relation was vastly simplified last year. But a further simplification was made possible last week, thus arriving to Painleve I. I will review many trivialities and lies about this famous non-linear differential equation, from a post modern point of view.

- Series
- Dissertation Defense
- Time
- Tuesday, November 11, 2008 - 13:30 for 2 hours
- Location
- Skiles 269
- Speaker
- Stephen Young – School of Mathematics, Georgia Tech

- Series
- PDE Seminar
- Time
- Tuesday, November 11, 2008 - 15:15 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Anna Mazzucato – Penn State University, State College

We discuss the inverse problem of determining elastic parameters in the interior of an anisotropic elastic media from dynamic measurements made at the surface. This problem has applications in medical imaging and seismology. The boundary data is modeled by the Dirichlet-to-Neumann map, which gives the correspondence between surface displacements and surface tractions. We first show that, without a priori information on the anisotropy type, uniqueness can hold only up to change of coordinates fixing the boundary. In particular, we study orbits of elasticity tensors under diffeomorphisms. Then, we obtain partial uniqueness for special classes of transversely isotropic media. This is joint work with L. Rachele (RPI).

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, November 12, 2008 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Benjamin Ridenhour – CDC/CCID/NCIRD, CTR

Parent-offspring interactions lead to natural conflicts. Offspring want as many resources as possible from parents in order to gain maximal fitness levels. On the other hand, parents desire to invest only enough to guarantee survival to reproduction. The resolution of the parent-offspring conflict has been a topic of much debate in evolutionary biology and typically invoke the concept of 'costs' to begging by offspring. Here I present the analysis of a simple quantitative genetic model of parent-offspring interactions that does not costs to resolve parent-offspring conflicts.

- Series
- ACO Student Seminar
- Time
- Wednesday, November 12, 2008 - 13:30 for 2 hours
- Location
- Skiles 269
- Speaker
- Gagan Goel – ACO Computer Science, Georgia Tech

We consider the following Maximum Budgeted Allocation(MBA) problem: Given a set of m indivisible items and n agents; each agent i is willing to pay b_ij amount of money on item j, and in addition he species the maximum amount (budget of B_i) he is willing to pay in total over all the items he receives. Goal is to allocate items to agents so as to maximize the total payment received from all the agents. The problem naturally arises as auctioneer revenue maximization in first price budget-constrained Auctions (For e.g. auctioning of TV/Radio ads by Google). Our main results are: 1) We give a 3/4-approximation algorithm for MBA improving upon the previous best of 0.632 [Anelman-Mansour, 04]. Our factor matches the integrality gap of the LP used by the previous results. 2) We prove it is NP-hard to approximate MBA to any factor better than 15/16, previously only NP-hardness was known. Our result also implies NP-hardness of approximating maximum submodular welfare with demand oracle to a factor better than 15/16, improving upon the best known hardness of 275/276 [Feige-Vondrak, 07]. Our hardness techniques can be modified to prove that it is NP-hard to approximate the Generalized Assignment Problem (GAP) to any factor better than 10/11. This improves upon the 422/423 hardness of [Chekuri-Kumar, 04]. We use iterative rounding on a natural LP relaxation of MBA to obtain the 3/4-approximation. Recently iterative rounding has achieved considerable success in designing approximation algorithms. However, these successes have been limited to minimization problems, and as per our knowledge, this work is the first iterative rounding based approximation algorithm for a natural maximization problem. We also give a (3/4 - \epsilon)-factor algorithm based on the primal-dual schema which runs in O(nm) time, for any constant \epsilon > 0. In this talk, I will present the iterative rounding based algorithm, show the hardness reductions, and put forward some directions which can help in solving the natural open question of closing the approximation gap. Joint work with Deeparnab Chakrabarty.

- Series
- Mathematical Finance/Financial Engineering Seminar
- Time
- Wednesday, November 12, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Christian Houdré – School of Mathematics, Georgia Tech

In connection with the class Stochastic Processes in Finance II, we will have a supplementary lecture where a first, 50 minutes long, movie on Doeblin's life will be shown. This will be followed by a second movie, 30 minutes long, where Yor explains on the blackboard Doeblin's contribution to what Shreeve calls the Ito-Doeblin's lemma.

- Series
- Stochastics Seminar
- Time
- Thursday, November 13, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Anssi Yli-Jyrä – Helsink University

Many context-free formalisms based on transitive properties of trees and strings have been converted to probabilitic models. We have Probabilistic Finite Automaton, Probabilistic Context Free Grammar and Probabilistic Tree Adjoining Grammars and many other probabilistic models of grammars. Typically such formalisms employ context-free productions that are transitively closed. Context-free grammars can be represented declaratively through context-sensitive grammars that analyse or check wellformedness of trees. When this direction is elaborated further, we obtain constraint-based representations for regular, context-free and mildly-context sensitive languages and their associated structures. Such representations can also be Probabilistic and this could be achieved by combining weighted rational operations and Dyck languages. More intuitively, the rational operations are packed to a new form of conditional rule: Generalized Restriction or GR in short (Yli-Jyrä and Koskenniemi 2004), or a predicate logic over strings. The conditional rule, GR, is flexible and provides total contexts, which is very useful e.g. when compiling rewriting rules for e.g. phonological alternations or speech or text normalization. However, the total contexts of different conditional rewriting rules can overlap. This implies that the conditions of different rules are not independent and the probabilities do not combine like in the case of context-free derivations. The non-transitivity causes problems for the general use of probabilistic Generalized Restriction e.g. when adding probabilities to phonological rewriting grammars that define regular relations.

- Series
- ACO Distinguished Lecture
- Time
- Thursday, November 13, 2008 - 16:30 for 2 hours
- Location
- Klaus 1116
- Speaker
- Harold W. Kuhn – Princeton University

RECEPTION TO FOLLOW

Fifty five years ago, two results of the Hungarian mathematicians, Koenig and Egervary, were combined using the duality theory of linear programming to construct the Hungarian Method for the Assignment Problem. In a recent reexamination of the geometric interpretation of the algorithm (proposed by Schmid in 1978) as a steepest descent method, several variations on the algorithm have been uncovered, which seem to deserve further study.
The lecture will be self-contained, assuming little beyond the duality theory of linear programming. The Hungarian Method will be explained at an elementary level and will be illustrated by several examples.
We shall conclude with account of a posthumous paper of Jacobi containing an algorithm developed by him prior to 1851 that is essentially identical to the Hungarian Method, thus anticipating the results of Koenig (1931), Egervary (1931), and Kuhn (1955) by many decades.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, November 14, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Thang Le – School of Mathematics, Georgia Tech

We will explain the famous result of Luck and Schick which says that for a large class of 3-manifolds, including all knot complements, the hyperbolic volume is equal to the l^2-torsion. Then we speculate about the growth of homology torsions of finite covers of knot complements. The talk will be elementary and should be accessible to those interested in geometry/topology.

- Series
- Stochastics Seminar
- Time
- Friday, November 14, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Sayan Mukherjee – Department of Statistical Science, Duke University

Let X=(X_1,\ldots,X_n) be a n-dimensional random vector for which the distribution has Markov structure corresponding to a junction forest, assuming functional forms for the marginal distributions associated with the cliques of the underlying graph. We propose a latent variable approach based on computing junction forests from filtrations. This methodology establishes connections between efficient algorithms from Computational Topology and Graphical Models, which lead to parametrizations for the space of decomposable graphs so that: i) the dimension grows linearly with respect to n, ii) they are convenient for MCMC sampling.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, November 17, 2008 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Maoan Han – Shanghai Normal University

Let H(m) denote the maximal number of limit cycles of polynomial systems of degree m. It is called the Hilbert number. The main part of Hilbert's 16th problem posed in 1902 is to find its value. The problem is still open even for m=2. However, there have been many interesting results on the lower bound of it for m\geq 2. In this paper, we give some new lower bounds of this number. The results obtained in this paper improve all existing results for all m\geq 7 based on some known results for m=3,4,5,6. In particular, we confirm the conjecture H(2k+1) \geq (2k+1)^2-1 and obtain that H(m) grows at least as rapidly as \frac{1}{2\ln2}(m+2)^2\ln(m+2) for all large m.

- Series
- CDSNS Colloquium
- Time
- Monday, November 17, 2008 - 16:30 for 2 hours
- Location
- Skiles 255
- Speaker
- Jibin Li – Kunming Univeristy of Science and Technology and Zhejiang Normal University

Nonlinear wave phenomena are of great importance in the physical world and have been for a long time a challenging topic of research for both pure and applied mathematicians. There are numerous nonlinear evolution equations for which we need to analyze the properties of the solutions for time evolution of the system. As the first step, we should understand the dynamics of their traveling wave solutions. There exists an enormous literature on the study of nonlinear wave equations, in which exact explicit solitary wave, kink wave, periodic wave solutions and their dynamical stabilities are discussed. To find exact traveling wave solutions for a given nonlinear wave system, a lot of methods have been developed. What is the dynamical behavior of these exact traveling wave solutions? How do the travelling wave solutions depend on the parameters of the system? What is the reason of the smoothness change of traveling wave solutions? How to understand the dynamics of the so-called compacton and peakon solutions? These are very interesting and important problems. The aim of this talk is to give a more systematic account for the bifurcation theory method of dynamical systems to find traveling wave solutions and understand their dynamics for two classes of singular nonlinear traveling systems.

- Series
- PDE Seminar
- Time
- Tuesday, November 18, 2008 - 15:15 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Robin Young – University of Massachusetts, Amherst

We consider the existence of periodic solutions to the Euler equations of gas dynamics. Such solutions have long been thought not to exist due to shock formation, and this is confirmed by the celebrated Glimm-Lax decay theory for 2x2 systems. However, in the full 3x3 system, multiple interaction effects can combine to slow down and prevent shock formation. In this talk I shall describe the physical mechanism supporting periodicity, describe combinatorics of simple wave interactions, and develop periodic solutions to a "linearized" problem. These linearized solutions have a beautiful structure and exhibit several surprising and fascinating phenomena. I shall also discuss partial progress on the perturbation problem: this leads us to problems of small divisors and KAM theory. This is joint work with Blake Temple.

- Series
- Research Horizons Seminar
- Time
- Wednesday, November 19, 2008 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Silas Alben – School of Mathematics, Georgia Tech

We examine some problems in the coupled motions of fluids and flexible solid bodies. We first present some basic equations in fluid dynamics and solid mechanics, and then show some recent asymptotic results and numerical simulations. No prior experience with fluid dynamics is necessary.

- Series
- ACO Student Seminar
- Time
- Wednesday, November 19, 2008 - 13:30 for 2 hours
- Location
- ISyE Executive Classroom
- Speaker
- Lei Wang – ACO Student, School of Mathematics, Georgia Tech

Nash bargaining was first modeled in John Nash's seminal 1950 paper. In his paper, he used a covex program to give the Nash bargaining solution, which satifies many nature properties. Recently, V.Vazirani defined a class of Nash bargaining problem as Uniform Nash Bargaining(UNB) and also defined a subclass called Submodular Nash Bargaining (SNB). In this talk, we will consider some game theoretic issues of UNB: (1) price of bargaining; (2) fully competitiveness; (3) min-max and max-min fairness and we show that each of these properties characterizes the subclass SNB.

- Series
- Analysis Seminar
- Time
- Thursday, November 20, 2008 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Dmitriy Bilyk – IAS &amp; U South Carolina

Note change in time.

The theory of geometric discrepancy studies different variations of the following question: how well can one approximate a uniform distribution by a discrete one, and what are the limitations that necessarily arise in such approximations. Historically, the methods of harmonic analysis (Fourier transform, Fourier series, wavelets, Riesz products etc) have played a pivotal role in the subject. I will give an overview of the problems, methods, and results in the field and discuss some latest developments.

- Series
- Graph Theory Seminar
- Time
- Thursday, November 20, 2008 - 12:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Carl Yerger – School of Mathematics, Georgia Tech

Given a configuration of pebbles on the vertices of a connected graph G, a pebbling move is defined as the removal of two pebbles from some vertex, and the placement of one of these on an adjacent vertex. The pebbling number of a graph G is the smallest integer k such that given any configuration of k pebbles on G and any specified vertex v in V(G), there is a sequence of pebbling moves that sends a pebble to v. We will show that the pebbling number of a graph of diameter four on n vertices is at most 3n/2 + O(1), and this bound is best possible up to an additive constant. This proof, based on a discharging argument and a decomposition of the graph into ''irreducible branches'', generalizes work of Bukh on graphs of diameter three. Further, we prove that the pebbling number of a graph on n vertices with diameter d is at most (2^{d/2} - 1)n + O(1). This also improves a bound of Bukh.

- Series
- Stochastics Seminar
- Time
- Thursday, November 20, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Jian-Jian Ren – Department of Mathematics, University of Central Florida

So far, likelihood-based interval estimate for quantiles has not been studied in literature for interval censored Case 2 data and partly interval-censored data, and in this context the use of smoothing has not been considered for any type of censored data. This article constructs smoothed weighted empirical likelihood ratio confidence intervals (WELRCI) for quantiles in a unified framework for various types of censored data, including right censored data, doubly censored data, interval censored data and partly interval-censored data. The 4th-order expansion of the weighted empirical log-likelihood ratio is derived, and the 'theoretical' coverage accuracy equation for the proposed WELRCI is established, which generally guarantees at least the 'first-order' accuracy. In particular for right censored data, we show that the coverage accuracy is at least O(n^{-1/2}), and our simulation studies show that in comparison with empirical likelihood-based methods, the smoothing used in WELRCI generally gives a shorter confidence interval with comparable coverage accuracy. For interval censored data, it is interesting to find that with an adjusted rate n^{-1/3}, the weighted empirical log-likelihood ratio has an asymptotic distribution completely different from that by the empirical likelihood approach, and the resulting WELRCI perform favorably in available comparison simulation studies.

- Series
- Geometry Topology Seminar
- Time
- Friday, November 21, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Ken Baker – University of Miami

Lickorish observed a simple way to make two knots in S^3 that produced the same manifold by the same surgery. Many have extended this result with the most dramatic being Osoinach's method (and Teragaito's adaptation) of creating infinitely many distinct knots in S^3 with the same surgery yielding the same manifold. We will turn this line of inquiry around and examine relationships within such families of corresponding knots in the resulting surgered manifold.

- Series
- Combinatorics Seminar
- Time
- Friday, November 21, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Nick Zhao – University of Central Florida

In 1968, Vizing proposed the following conjecture which claims that if G is an edge chromatic critical graph with n vertices, then the independence number of G is at most n/2. In this talk, we will talk about this conjecture and the progress towards this conjecture.

- Series
- PDE Seminar
- Time
- Friday, November 21, 2008 - 16:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Athanasios Tzavaras – Univeristy of Maryland

We consider a system of hyperbolic-parabolic equations describing the material instability mechanism associated to the formation of shear bands at high strain-rate plastic deformations of metals. Systematic numerical runs are performed that shed light on the behavior of this system on various parameter regimes. We consider then the case of adiabatic shearing and derive a quantitative criterion for the onset of instability: Using ideas from the theory of relaxation systems we derive equations that describe the effective behavior of the system. The effective equation turns out to be a forward-backward parabolic equation regularized by fourth order term (joint work with Th. Katsaounis and Th. Baxevanis, Univ. of Crete).

- Series
- Analysis Seminar
- Time
- Monday, November 24, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Ignacio Uriarte-tuero – Michigan State University

In his celebrated paper on area distortion under planar quasiconformal mappings (Acta 1994), K. Astala proved that a compact set E of Hausdorff dimension d is mapped under a K-quasiconformal map f to a set fE of Hausdorff dimension at most d' = \frac{2Kd}{2+(K-1)d}, and he proved that this result is sharp. He conjectured (Question 4.4) that if the Hausdorff measure \mathcal{H}^d (E)=0, then \mathcal{H}^{d'} (fE)=0. This conjecture was known to be true if d'=0 (obvious), d'=2 (Ahlfors), and more recently d'=1 (Astala, Clop, Mateu, Orobitg and UT, Duke 2008.) The approach in the last mentioned paper does not generalize to other dimensions. Astala's conjecture was shown to be sharp (if it was true) in the class of all Hausdorff gauge functions in work of UT (IMRN, 2008). Finally, we (Lacey, Sawyer and UT) jointly proved completely Astala's conjecture in all dimensions. The ingredients of the proof come from Astala's original approach, geometric measure theory, and some new weighted norm inequalities for Calderon-Zygmund singular integral operators which cannot be deduced from the classical Muckenhoupt A_p theory. These results are intimately related to (not yet fully understood) removability problems for various classes of quasiregular maps. The talk will be self-contained.

- Series
- Geometry Topology Seminar
- Time
- Monday, November 24, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Sa'ar Hersonsky – University of Georgia

Cannon: "A f.g. negatively curved group with boundary homeomorphic to the round two sphere is Kleinian". We shall outline a combinatorial (complex analysis motivated) approach to this interesting conjecture (following Cannon, Cannon-Floyd-Parry). If time allows we will hint on another approach (Bonk-Kleiner) (as well as ours). The talk should be accessible to graduate students with solid background in: complex analysis, group theory and basic topology.

- Series
- Stochastics Seminar
- Time
- Tuesday, November 25, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Nizar Demni – University of Bielefeld

We will introduce the Dunkl derivative as well as the Dunkl process and some of its properties. We will treat its radial part called the radial Dunkl process and light the connection to the eigenvalues of some matrix valued processes and to the so called Brownian motions in Weyl chambers. Some open problems will be discussed at the end.

- Series
- PDE Seminar
- Time
- Tuesday, November 25, 2008 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Bojan Popov – Texas A&amp;M University

In this talk we will consider three different numerical methods for solving nonlinear PDEs:

- A class of Godunov-type second order schemes for nonlinear conservation laws, starting from the Nessyahu-Tadmor scheme;
- A class of L1 -based minimization methods for solving linear transport equations and stationary Hamilton- Jacobi equations;
- Entropy-viscosity methods for nonlinear conservation laws.

All of the above methods are based on high-order approximations of the corresponding nonlinear PDE and respect a weak form of an entropy condition. Theoretical results and numerical examples for the performance of each of the three methods will be presented.

- Series
- ACO Student Seminar
- Time
- Wednesday, November 26, 2008 - 13:30 for 2 hours
- Location
- ISyE Executive Classroom
- Speaker
- Juan Pablo Vielma – ISyE, Georgia Tech

Two independent proofs of the polyhedrality of the split closure of Mixed Integer Linear Program have been previously presented. Unfortunately neither of these proofs is constructive. In this paper, we present a constructive version of this proof. We also show that split cuts dominate a family of inequalities introduced by Koppe and Weismantel.

- Series
- Analysis Seminar
- Time
- Wednesday, November 26, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Yoshihiro Sawano – Gakushuin University, Japan

Note time change.

Let I_\alpha be the fractional integral operator. The Olsen inequality, useful in certain PDEs, concerns multiplication operators and fractional integrals in the L^p-norm, or more generally, the Morrey norm. We strenghten this inequality from the one given by Olsen.

- Series
- Analysis Seminar
- Time
- Monday, December 1, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Sergey Tikhonov – ICREA and CRM, Barcelona

In this talk we will discuss a generalization of monotone sequences/functions as well as of those of bounded variation. Some applications to various problems of analysis (the Lp-convergence of trigonometric series, the Boas-type problem for the Fourier transforms, the Jackson and Bernstein inequalities in approximation, etc.) will be considered.

- Series
- Geometry Topology Seminar
- Time
- Monday, December 1, 2008 - 14:30 for 2 hours
- Location
- Skiles 269
- Speaker
- Sandra Ritz – University of South Carolina

We will begin with an overview of the Burau representation of the braid group. This will be followed by an introduction to a contact category on 3-manifolds, with a brief discussion of its relation to the braid group.

- Series
- Geometry Topology Seminar
- Time
- Monday, December 1, 2008 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Yanki Lekili – MIT

A broken fibration is a map from a smooth 4-manifold to S^2 with isolated Lefschetz singularities and isolated fold singularities along circles. These structures provide a new framework for studying the topology of 4-manifolds and a new way of studying Floer theoretical invariants of low dimensional manifolds. In this talk, we will first talk about topological constructions of broken Lefschetz fibrations. Then, we will describe Perutz's 4-manifold invariants associated with broken fibrations and a TQFT-like structure corresponding to these invariants. The main goal of this talk is to sketch a program for relating these invariants to Ozsváth-Szabó invariants.

- Series
- PDE Seminar
- Time
- Tuesday, December 2, 2008 - 15:15 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Gary M. Lieberman – Iowa State University

The usual boundary condition adjoined to a second order elliptic equation is the Dirichlet problem, which prescribes the values of the solution on the boundary. In many applications, this is not the natural boundary condition. Instead, the value of some directional derivative is given at each point of the boundary. Such problems are usually considered a minor variation of the Dirichlet condition, but this talk will show that this problem has a life of its own. For example, if the direction changes continuously, then it is possible for the solution to be continuously differentiable up to a merely Lipschitz boundary. In addition, it's possible to get smooth solutions when the direction changes discontinuously as well.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, December 3, 2008 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Andrei Fedorov – School of Mechanical Engineering, Georgia Tech

In this presentation I will outline physical principles of two analytical techniques, the Scanning ElectroChemical Microscopy (SECM) and Scanning Mass Spectrometry (SMS), which can be used to obtain the spatially resolved images of (bio/electro)chemically active interfaces. The mathematical models need to be employed for image interpretation and mapping measured quantities (e.g., an electrode current in SECM) to biochemically relevant quantities (e.g., kinetics of exocytotic signaling events in cellular communications), and I will review the key ideas/assumptions used for the model formulation and the main results of analysis and simulations. In conclusion, an alternative approach to spatially-resolved imaging based on the multi-probe array will be introduced along with intriguing opportunities and challenges for mathematical interpretation of such images.

- Series
- Combinatorics Seminar
- Time
- Friday, December 5, 2008 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Luis Rademacher – School of Computer Science, Georgia Tech

Expanders via Random Spanning Trees Motivated by the problem of routing reliably and scalably in a graph, we introduce the notion of a splicer, the union of spanning trees of a graph. We prove that for any bounded-degree n-vertex graph, the union of two random spanning trees approximates the expansion of every cut of the graph to within a factor of O(log n). For the random graph G_{n,p}, for p > c (log n)/n, two spanning trees give an expander. This is suggested by the case of the complete graph, where we prove that two random spanning trees give an expander. The construction of the splicer is elementary — each spanning tree can be produced independently using an algorithm by Aldous and Broder: a random walk in the graph with edges leading to previously unvisited vertices included in the tree. A second important application of splicers is to graph sparsification where the goal is to approximate every cut (and more generally the quadratic form of the Laplacian) using only a small subgraph of the original graph. Benczur-Karger as well as Spielman-Srivastava have shown sparsifiers with O(n log n/eps^2) edges that achieve approximation within factors 1+eps and 1-eps. Their methods, based on independent sampling of edges, need Omega(n log n) edges to get any approximation (else the subgraph could be disconnected) and leave open the question of linear-size sparsifiers. Splicers address this question for random graphs by providing sparsifiers of size O(n) that approximate every cut to within a factor of O(log n). This is joint work with Navin Goyal and Santosh Vempala.

- Series
- PDE Seminar
- Time
- Thursday, December 11, 2008 - 15:15 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Robert Finn – Stanford University

We calculate numerically the solutions of the stationary Navier-Stokes equations in two dimensions, for a square domain with particular choices of boundary data. The data are chosen to test whether bounded disturbances on the boundary can be expected to spread into the interior of the domain. The results indicate that such behavior indeed can occur, but suggest an estimate of general form for the magnitudes of the solution and of its derivatives, analogous to classical bounds for harmonic functions. The qualitative behavior of the solutions we found displayed some striking and unexpected features. As a corollary of the study, we obtain two new examples of non-uniqueness for stationary solutions at large Reynolds numbers.

- Series
- Other Talks
- Time
- Friday, December 12, 2008 - 09:00 for 8 hours (full day)
- Location
- Skiles 243
- Speaker
- Various Speakers – Various Universities

The Southeast Geometry Seminar (SGS) is a semiannual series of one day events organized by Vladimir Oliker (Emory), Mohammad Ghomi and John McCuan (Georgia Tech) and Gilbert Weinstein (UAB). See http://www.math.uab.edu/sgs for details

- Series
- Stochastics Seminar
- Time
- Friday, December 12, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Joel Zinn – Texas A&amp;M University

In this approach to the Gaussian Correlation Conjecture we must check the log-concavity of the moment generating function of certain measures pulled down by a particular Gaussian density.

- Series
- Job Candidate Talk
- Time
- Wednesday, January 7, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Mike Zieve – IAS

I will present properties of polynomials mappings and generalizations. I will first describe all polynomials f and g for which there is a complex number c such that the orbits {c, f(c), f(f(c)), ...} and {c, g(c), g(g(c)), ...} have infinite intersection. I will also discuss a common generalization of this result and Mordell's conjecture (Faltings' theorem). After this I will move to polynomial mappings over finite fields, with connections to curves having large automorphism groups and instances of a positive characteristic analogue of Riemann's existence theorem.

- Series
- Job Candidate Talk
- Time
- Thursday, January 8, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Noureddine El Karoui – UC Berkeley

It is now increasingly common in statistical practice to encounter datasets in which the number of observations, n, is of the same order of magnitude as the number of measurements, p, we have per observation. This simple remark has important consequences for theoretical (and applied) statistics. Namely, it suggests on the theoretical front that we should study the properties of statistical procedures in an asymptotic framework where p and n both go to infinity (and p/n has for instance a finite non-zero limit). This is drastically different from the classical theory where p is held fixed when n goes to infinity. Since a number of techniques in multivariate statistics rely fundamentally on sample covariance matrices and their eigenvalues and eigenvectors, the spectral properties of large dimensional covariance matrices play a key role in such "large n, large p" analyses. In this talk, I will present a few problems I have worked on, concerning different aspects of the interaction between random matrix theory and multivariate statistics. I will discuss some fluctuation properties of the largest eigenvalue of sample covariance matrices when the population covariance is (fairly) general, talk about estimation problems for large dimensional covariance matrices and, time permitting, address some applications in a classic problem of mathematical finance. The talk will be self-contained and no prior knowledge of statistics or random matrix theory will be assumed.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, January 12, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Frank Crosby – Naval Surface Warfare Center, Panama City

Several imaging innovations have been designed to find hidden objects in coastal areas of entry, such as beaches and ports. Each imaging device is designed to exploit particular distinguishing characteristics. This talk with cover using a tunable multi-spectral camera for polarization based detection and object identification with a flash LIDAR camera that produces three-dimensional imagery.

- Series
- Math Physics Seminar
- Time
- Monday, January 12, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Robert Seiringer – Princeton University

We present an overview of mathematical results on the low temperature properties of dilute quantum gases, which have been obtained in the past few years. The discussion includes, for instance, results on the free energy in the thermodynamic limit, and on Bose-Einstein condensation, Superfluidity and quantized vortices in trapped gases. All these properties are intensely being studied in current experiments on cold atomic gases. We will give a brief description of the mathematics involved in understanding these phenomena, starting from the underlying many-body Schroedinger equation.

- Series
- Research Horizons Seminar
- Time
- Wednesday, January 14, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Stavros Garoufalidis – School of Mathematics, Georgia Tech

The Apery sequence is a sequence of natural numbers 1,5,73,1445,...which is used to prove the irrationality of zeta(3). Can you compute its asymptotic expansion to all orders of 1/n? The talk will not assume a lot, but promises to compute, and also justify.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, January 15, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Igor Pritzker – Oklahoma State University

Issai Schur (1918) considered a class of polynomials with integer coefficients and simple zeros in the closed unit disk. He studied the limit behavior of the arithmetic means s_n for zeros of such polynomials as the degree n tends to infinity. Under the assumption that the leading coefficients are bounded, Schur proved that \limsup_{n\to\infty} |s_n| \le 1-\sqrt{e}/2. We show that \lim_{n\to\infty} s_n = 0 as a consequence of the asymptotic equidistribution of zeros near the unit circle. Furthermore, we estimate the rate of convergence of s_n to 0. These results follow from our generalization of the Erdos-Turan theorem on discrepancy in angular equidistribution of zeros. We give a range of applications to polynomials with integer coefficients. In particular, we show that integer polynomials have some unexpected restrictions of growth on the unit disk. Schur also studied problems on means of algebraic numbers on the real line. When all conjugate algebraic numbers are positive, the problem of finding \liminf_{n\to\infty} s_n was developed further by Siegel and many others. We provide a solution of this problem for algebraic numbers equidistributed in subsets of the real line.

- Series
- Graph Theory Seminar
- Time
- Thursday, January 15, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Hein van der Holst – Eindhoven University of Technology

Each graph can be embedded in 3-space. The problem becomes more interesting if we put restrictions on the type of embedding. For example, a linkless embedding of a graph is one where each pair of vertex-disjoint circuits has linking number equal to zero. The class of all graphs that have a linkless embedding is closed under taking minors. Robertson, Seymour, and Thomas gave the forbidden minors for this class of graphs. Open remained how to find a linkless embedding in polynomial time. In the talk we start with discussing an algorithm to find a linkless embedding.Instead of embedding the graph in 3-space, we could also consider mapping properties of certain superstructures of the graph in 3-space, and, indeed, if this superstructure has not the right mapping properties in 3-space, see whether it has the right one in 4-space, etc. Recently, we introduced for a graph G a new graph parameter \sigma(G), which is defined as the smallest d such that superstructures of G have a zero intersection mapping in d-space. The nicest property of this graph parameter is its independence of the superstructure and thus depends on the graph only. For d=2 and d=3, \sigma(G) \leq d if and only if G is outerplanar and planar, respectively. The graphs G with \sigma(G)\leq 4 are exactly those that have a linkless embedding. In the second part of the talk we will discuss this new graph parameter. (This part is joint work with R. Pendavingh.)

- Series
- Job Candidate Talk
- Time
- Thursday, January 15, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Carina Curto – Mathematics Department, New York University

We construct our understanding of the world solely from neuronal activity generated in our brains. How do we do this? Many studies have investigated how the electrical activity of neurons (action potentials) is related to outside stimuli, and maps of these relationships -- often called receptive fields -- are routinely computed from data collected in neuroscience experiments. Yet how the brain can understand the meaning of this activity, without the dictionary provided by these maps, remains a mystery. I will present some recent results on this question in the context of hippocampal place cells -- i.e., neurons in rodent hippocampus whose activity is strongly correlated to the animal's position in space. In particular, we find that topological and geometric features of the animal's physical environment can be derived purely from the activity of hippocampal place cells. Relating stimulus space topology and geometry to neural activity opens up new opportunities for investigating the connectivity of recurrent networks in the brain. I will conclude by discussing some current projects along these lines.

- Series
- Stochastics Seminar
- Time
- Thursday, January 15, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Alexey Chervonenkis – Russian Academy of Sciences and Royal Holloway University of London

The uniform convergence of empirical averages to their expectations for a set of bounded test functions will be discussed. In our previous work, we proved a necessary and sufficient condition for the uniform convergence that can be formulated in terms of the epsilon-entropy of certain sets associated to the sample. In this talk, I will consider the case where that condition is violated. The main result is that in this situation strong almost sure oscillations take place. In fact, with probability one, for a given oscillation pattern, one can find an admissible test function that realizes this pattern for any positive prescribed precision level.

- Series
- Other Talks
- Time
- Friday, January 16, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Klaus 2447
- Speaker
- Alexey Chervonenkis – Russian Academy of Science and Royal Holloway University of London

It is shown (theoretically and empirically) that a reliable result can be gained only in the case of a certain relation between the capacity of the class of models from which we choose and the size of the training set. There are different ways to measure the capacity of a class of models. In practice the size of a training set is always finite and limited. It leads to an idea to choose a model from the most narrow class, or in other words to use the simplest model (Occam's razor). But if our class is narrow, it is possible that there is no true model within the class or a model close to the true one. It means that there will be greater residual error or larger number of errors even on the training set. So the problem of model complexity choice arises – to find a balance between errors due to limited number of training data and errors due to excessive model simplicity. I shall review different approaches to the problem.

- Series
- Job Candidate Talk
- Time
- Friday, January 16, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Aaron Levin – Scuola Normale Superiore Pisa

After introducing and reviewing the situation for rational and integral points on curves, I will discuss various aspects of integral points on higher-dimensional varieties. In addition to discussing recent higher-dimensional results, I will also touch on connections with the value distribution theory of holomorphic functions and give some concrete open problems.

- Series
- Job Candidate Talk
- Time
- Friday, January 16, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Aaron Levin – Scuola Normale Superiore Pisa

After introducing and reviewing the situation for rational and integral points on curves, I will discuss various aspects of integral points on higher-dimensional varieties. In addition to discussing recent higher-dimensional results, I will also touch on connections with the value distribution theory of holomorphic functions and give some concrete open problems.

- Series
- Other Talks
- Time
- Friday, January 16, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Klaus 2447
- Speaker
- Vladimir Vapnik – NEC Laboratories, Columbia University and Royal Holloway University of London

<p>You are cordially invited to attend a reception that will follow the seminar to chat informally with faculty and students. Refreshments will be provided.</p>

The existing machine learning paradigm considers a simple scheme: given a set of training examples find in a given collection of functions the one that in the best possible way approximates the unknown decision rule. In such a paradigm a teacher does not play an important role. In human learning, however, the role of a teacher is very important: along with examples a teacher provides students with explanations, comments, comparisons, and so on. In this talk I will introduce elements of human teaching in machine learning. I will consider an advanced learning paradigm called learning using hidden information (LUHI), where at the training stage a teacher gives some additional information x^* about training example x. This information will not be available at the test stage. I will consider the LUHI paradigm for support vector machine type of algorithms, demonstrate its superiority over the classical one and discuss general questions related to this paradigm. For details see FODAVA, Foundations of Data Analysis and Visual Analytics

- Series
- PDE Seminar
- Time
- Friday, January 16, 2009 - 16:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Benoit Perthame – Université Pierre et Marie Curie, Paris

Living systems are subject to constant evolution through the two processes of mutations and selection, a principle discovered by Darwin. In a very simple, general, and idealized description, their environment can be considered as a nutrient shared by all the population. This allows certain individuals, characterized by a 'phenotypical trait', to expand faster because they are better adapted to the environment. This leads to select the 'best fitted trait' in the population (singular point of the system). On the other hand, the new-born population undergoes small variance on the trait under the effect of genetic mutations. In these circumstances, is it possible to describe the dynamical evolution of the current trait?
We will give a mathematical model of such dynamics, based on parabolic equations, and show that an asymptotic method allows us to formalize precisely the concepts of monomorphic or polymorphic population. Then, we can describe the evolution of the 'best fitted trait' and eventually compute various forms of branching points, which represent the cohabitation of two different populations.
The concepts are based on the asymptotic analysis of the above mentioned parabolic equations, one appropriately rescaled. This leads to concentrations of the solutions and the difficulty is to evaluate the weight and position of the moving Dirac masses that describe the population. We will show that a new type of Hamilton-Jacobi equation, with constraints, naturally describes this asymptotic. Some additional theoretical questions as uniqueness for the limiting H.-J. equation will also be addressed.
This work is based on collaborations with O. Diekmann, P.-E. Jabin, S. Mischler, S. Cuadrado, J. Carrillo, S. Genieys, M. Gauduchon and G. Barles.

- Series
- Job Candidate Talk
- Time
- Tuesday, January 20, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Anton Leykin – University of Illinois at Chicago

Numerical algebraic geometry provides a collection of novel methods to treat the solutions of systems of polynomial equations. These hybrid symbolic-numerical methods based on homotopy continuation technique have found a wide range of applications in both pure and applied areas of mathematics. This talk gives an introduction to numerical algebraic geometry and outlines directions in which the area has been developing. Two topics are highlighted: (1) computation of Galois groups of Schubert problems, a recent application of numerical polynomial homotopy continuation algorithms to enumerative algebraic geometry; (2) numerical primary decomposition, the first numerical method that discovers embedded solution components.

- Series
- ACO Colloquium
- Time
- Wednesday, January 21, 2009 - 16:30 for 2 hours
- Location
- Klaus
- Speaker
- Michael Mitzenmacher – Harvard University

We describe recent progress in the study of the binary deletion channel and related channels with synchronization errors, including a clear description of many open problems in this area. As an example, while the capacity of the binary symmetric error channel and the binary erasure channel have been known since Shannon, we still do not have a closed-form description of the capacity of the binary deletion channel. We highlight a recent result that shows that the capacity is at least (1-p)/9 when each bit is deleted independently with fixed probability p.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, January 22, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Alexander Its – Indiana University-Purdue University Indianapolis

In this talk we will review some of the global asymptotic results obtained during the last two decades in the theory of the classical Painleve equations with the help of the Isomonodromy - Riemann-Hilbert method. The results include the explicit derivation of the asymptotic connection formulae, the explicit description of linear and nonlinear Stokes phenomenon and the explicit evaluation of the distribution of poles. We will also discuss some of the most recent results emerging due to the appearance of Painleve equations in random matrix theory. The Riemann-Hilbert method will be outlined as well.

- Series
- SIAM Student Seminar
- Time
- Friday, January 23, 2009 - 12:30 for 2 hours
- Location
- Skiles 269
- Speaker
- Linwei Xin – School of Mathematics, Georgia Tech

In this talk, I will focus on some interesting examples in the conditional expectation and martingale, for example, gambling system "Martingale", Polya's urn scheme, Galton-Watson process, Wright-Fisher model of population genetics. I will
skip the theorems and properties. Definitions to support the examples will be introduced. The talk will not assume a lot of probability, just some basic measure theory.

- Series
- Other Talks
- Time
- Friday, January 23, 2009 - 15:00 for 2 hours
- Location
- Skiles 269
- Speaker
- Mohammad Ghomi – School of Mathematics, Georgia Tech

h-Principle consists of a powerful collection of tools developed by Gromov and others to solve underdetermined partial differential equations or relations which arise in differential geometry and topology. In these talks I will describe the Holonomic approximation theorem of Eliashberg-Mishachev, and discuss some of its applications including the sphere eversion theorem of Smale. Further I will discuss the method of convex integration and its application to proving the C^1 isometric embedding theorem of Nash.

- Series
- Combinatorics Seminar
- Time
- Friday, January 23, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Gregg Musiker – MIT

In this talk, I will discuss chip-firing games on graphs, and the related Jacobian groups. Additionally, I will describe elliptic curves over finite fields, and how such objects also have group structures. For a family of graphs obtained by deforming the sequence of wheel graphs, the cardinalities of the Jacobian groups satisfy a nice reciprocal relationship with the orders of elliptic curves as we consider field extensions. I will finish by discussing other surprising ways that these group structures are analogous. Some of this research was completed as part of my dissertation work at the University of California, San Diego under Adriano Garsia's guidance.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, January 23, 2009 - 15:00 for 2 hours
- Location
- Skiles 269
- Speaker
- Mohammad Ghomi – Ga Tech

$h$-Principle consists of a powerful collection of tools developed by Gromov and others to solve underdetermined partial differential equations or relations which arise in differential geometry and topology. In these talks I will describe the Holonomic approximation theorem of Eliashberg-Mishachev, and discuss some of its applications including the sphere eversion theorem of Smale. Further I will discuss the method of convex integration and its application to proving the $C^1$ isometric embedding theorem of Nash.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, January 26, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Ming-Jun Lai – University of Georgia

I will first explain why we want to find the sparse solutions of underdetermined linear systems. Then I will explain how to solve the systems using \ell_1, OGA, and \ell_q approaches. There are some sufficient conditions to ensure that these solutions are the sparse one, e.g., some conditions based on restricted isometry property (RIP) by Candes, Romberg, and Tao'06 and Candes'08. These conditions are improved recently in Foucart and Lai'08. Furthermore, usually, Gaussian random matrices satisfy the RIP. I shall explain random matrices with strictly sub-Gaussian random variables also satisfy the RIP.

- Series
- CDSNS Colloquium
- Time
- Monday, January 26, 2009 - 16:30 for 2 hours
- Location
- Skiles 255
- Speaker
- Sergei Pilyugin – University of Florida

I will present a generalization of a classical within-host model of a viral infection that includes multiple strains of the virus. The strains are allowed to mutate into each other. In the absence of mutations, the fittest strain drives all other strains to extinction. Treating mutations as a small perturbation, I will present a global stability result of the perturbed equilibrium. Whether a particular strain survives is determined by the connectivity of the graph describing all possible mutations.

- Series
- Mathematical Finance/Financial Engineering Seminar
- Time
- Tuesday, January 27, 2009 - 11:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 269
- Speaker
- Philip Protter – Cornell University

- Series
- PDE Seminar
- Time
- Tuesday, January 27, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Sung Ha Kang – School of Mathematics, Georgia Tech

Image segmentation has been widely studied, specially since Mumford-Shah functional was been proposed. Many theoretical works as well as numerous extensions have been studied rough out the years. In this talk, I will focus on couple of variational models for multi-phase segmentation. For the first model, we propose a model built upon the phase transition model of Modica and Mortola in material sciences and a properly synchronized fitting term that complements it. For the second model, we propose a variational functional for an unsupervised multiphase segmentation, by adding scale information of each phase. This model is able to deal with the instability issue associated with choosing the number of phases for multiphase segmentation.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, January 28, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Mike Boots – University of Sheffield

- Series
- Research Horizons Seminar
- Time
- Wednesday, January 28, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Antoine Henrot – University of Nancy, France

In this talk, we give an insight into the mathematical topic of shape optimization. First, we give several examples of problems, some of them are purely academic and some have an industrial origin. Then, we look at the different mathematical questions arising in shape optimization. To prove the existence of a solution, we need some topology on the set of domains, together with good compactness and continuity properties. Studying the regularity and the geometric properties of a minimizer requires tools from classical analysis, like symmetrization. To be able to define the optimality conditions, we introduce the notion of derivative with respect to the domain. At last, we give some ideas of the different numerical methods used to compute a possible solution.

- Series
- ACO Student Seminar
- Time
- Wednesday, January 28, 2009 - 13:30 for 2 hours
- Location
- ISyE Executive Classroom
- Speaker
- Sangho Shim – ISyE, Georgia Tech

In this article, we disprove the uniform shortest path routing conjecture for vertex-transitive graphs by constructing an infinite family of counterexamples.

- Series
- Job Candidate Talk
- Time
- Thursday, January 29, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Brett Wick – University of South Carolina

Carleson's Corona Theorem from the 1960's has served as a major motivation for many results in complex function theory, operator theory and harmonic analysis. In its simplest form, the result states that for two bounded analytic functions, g_1 and g_2, on the unit disc with no common zeros, it is possible to find two other bounded analytic functions, f_1 and f_2, such that f_1g_1+f_2g_2=1. Moreover, the functions f_1 and f_2 can be chosen with some norm control. In this talk we will discuss an exciting new generalization of this result to certain function spaces on the unit ball in several complex variables. In particular, we will highlight the Corona Theorem for the Drury-Arveson space and its applications in multi-variable operator theory.

- Series
- Stochastics Seminar
- Time
- Thursday, January 29, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Yuri Bakhtin – School of Mathematics, Georgia Tech

This work began in collaboration with C.Heitsch. I will briefly discuss the biological motivation. Then I will introduce Gibbs random trees and study their asymptotics as the tree size grows to infinity. One of the results is a "thermodynamic limit" allowing to introduce a limiting infinite random tree which exhibits a few curious properties. Under appropriate scaling one can obtain a diffusion limit for the process of generation sizes of the infinite tree. It also turns out that one can approach the study the details of the geometry of the tree by tracing progenies of subpopulations. Under the same scaling the limiting continuum random tree can be described as a solution of an SPDE w.r.t. a Brownian sheet.

- Series
- SIAM Student Seminar
- Time
- Friday, January 30, 2009 - 12:30 for 2 hours
- Location
- Skiles 269
- Speaker
- Jinyong Ma – School of Mathematics, Georgia Tech

I plan to give a simple proof of the law of iterated logarithm in probability, which is a famous conclusion relative to strong law of large number, and in the proof I will cover the definition of some important notations in probability such as Moment generating function and large deviations, the proof is basically from Billingsley's book and I made some.

- Series
- Combinatorics Seminar
- Time
- Friday, January 30, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Kevin P. Costello – School of Mathematics, Georgia Tech

Part of Spielman and Teng's smoothed analysis of the Simplex algorithm relied on showing that most minors of a typical random rectangular matrix are well conditioned (do not have any singular values too close to zero). Motivated by this, Vershynin asked the question as to whether it was typically true that ALL minors of a random rectangular matrix are well conditioned. Here I will explain why that the answer to this question is in fact no: Even an n by 2n matrix will typically have n by n minors which have singular values exponentially close to zero.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, January 30, 2009 - 15:00 for 2 hours
- Location
- Skiles 269
- Speaker
- Mohammad Ghomi – Ga Tech

$h$-Principle consists of a powerful collection of tools developed by Gromov and others to solve underdetermined partial differential equations or relations which arise in differential geometry and topology. In these talks I will describe the Holonomic approximation theorem of Eliashberg-Mishachev, and discuss some of its applications including the sphere eversion theorem of Smale. Further I will discuss the method of convex integration and its application to proving the $C^1$ isometric embedding theorem of Nash. (Please note this course runs from 3-5.)

- Series
- Other Talks
- Time
- Friday, January 30, 2009 - 15:00 for 2 hours
- Location
- Skiles 269
- Speaker
- Mohammad Ghomi – School of Mathematics, Georgia Tech

Please note this course runs from 3-5.

h-Principle consists of a powerful collection of tools developed by Gromov and others to solve underdetermined partial differential equations or relations which arise in differential geometry and topology. In these talks I will describe the Holonomic approximation theorem of Eliashberg-Mishachev, and discuss some of its applications including the sphere eversion theorem of Smale. Further I will discuss the method of convex integration and its application to proving the C^1 isometric embedding theorem of Nash.

- Series
- Geometry Topology Seminar
- Time
- Monday, February 2, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- John Etnyre – School of Mathematics, Georgia Tech

I will discuss a "duality" among the linearized contact homology groups of a Legendrian submanifold in certain contact manifolds (in particular in Euclidean (2n+1)-space). This duality is expressed in a long exact sequence relating the linearized contact homology, linearized contact cohomology and the ordinary homology of the Legendrian submanifold. One can use this structure to ease difficult computations of linearized contact homology in high dimensions and further illuminate the proof of cases of the Arnold Conjecture for the double points of an exact Lagrangian in complex n- space.

- Series
- Analysis Seminar
- Time
- Monday, February 2, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Chris Heil – School of Mathematics, Georgia Tech

The Balian-Low Theorem is a strong form of the uncertainty principle for Gabor systems that form orthonormal or Riesz bases for L^2(R). In this talk we will discuss the Balian-Low Theorem in the setting of Schauder bases. We prove that new weak versions of the Balian-Low Theorem hold for Gabor Schauder bases, but we constructively demonstrate that several variants of the BLT can fail for Gabor Schauder bases that are not Riesz bases. We characterize a class of Gabor Schauder bases in terms of the Zak transform and product A_2 weights; the Riesz bases correspond to the special case of weights that are bounded away from zero and infinity. This is joint work with Alex Powell (Vanderbilt University).

- Series
- Job Candidate Talk
- Time
- Monday, February 2, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Dapeng Zhan – Yale University

Stochastic Loewner evolution (SLE) introduced by Oded Schramm is a breakthrough in studying the scaling limits of many two-dimensional lattice models from statistical physics. In this talk, I will discuss the proofs of the reversibility conjecture and duality conjecture about SLE. The proofs of these two conjectures use the same idea, which is to use a coupling technique to lift local couplings of two SLE processes that locally commute with each other to a global coupling. And from the global coupling, we can clearly see that the two conjectures hold.

- Series
- CDSNS Colloquium
- Time
- Monday, February 2, 2009 - 16:30 for 2 hours
- Location
- Skiles 255
- Speaker
- Pablo Laguna – School of Physics, Georgia Tech

I will review results from binary black hole simulations and the role that these simulations have in astrophysics and gravitational wave observations. I will then focus on the mathematical and computational aspects of the recent breakthroughs in numerical relativity that have made finding binary black hole solutions to the Einstein field equations an almost routine exercise.

- Series
- Mathematical Finance/Financial Engineering Seminar
- Time
- Tuesday, February 3, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Dmitry Kreslavskiy – Bloomberg

We will give an overview of the company as it relates to the work of a quant. We will discuss projects of interest, typical lifecycle of a project, and involved areas.

- Series
- PDE Seminar
- Time
- Tuesday, February 3, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Changfeng Gui – University of Connecticut

In this talk I will present Hamiltonian identities for elliptic PDEs and systems of PDEs. I will also show some interesting applications of these identities to problems related to solutions of some nonlinear elliptic equations in the entire space or plane. In particular, I will give a rigorous proof to the Young's law in triple junction configuration for a vector-valued Allen Cahn model arising in phase transition; a necessary condition for the existence of certain saddle solutions for Allen-Cahn equation with asymmetric double well potential will be derived, and the structure of level sets of general saddle solutions will also be discussed.

- Series
- Research Horizons Seminar
- Time
- Wednesday, February 4, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Sinem Celik Onaran – Department of Mathematics, Middle East Technical University

Due to Alexander, it is well known that every closed oriented 3-manifold has an open book decomposition. In this talk, we will define open book decompositions of 3-manifolds. We will discuss various examples and sketch the proof of Alexander's theorem. Further, we will discuss the importance of the open books in manifold theory, in particular in contact geometry.

- Series
- ACO Student Seminar
- Time
- Wednesday, February 4, 2009 - 13:30 for 2 hours
- Location
- ISyE Executive Classroom
- Speaker
- Richard Lipton – College Computing, Georgia Tech

Shrouded in mystery and kept hidden for decades, Richard Lipton's vault of open problems will be revealed...

- Series
- School of Mathematics Colloquium
- Time
- Thursday, February 5, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Alexander Shnirelman – Department of Mathematics, Concordia University

Consider the 2-d ideal incompressible fluid moving inside a bounded domain (say 2-d torus). It is described by 2-d Euler equations which have unique global solution; thus, we have a dynamical system in the space of sufficiently regular incompressible vector fields. The global properties of this system are poorly studied, and, as much as we know, paradoxical. It turns out that there exists a global attractor (in the energy norm), i.e. a set in the phase space attracting all trajectories (in spite the fact that the system is conservative). This apparent contradiction leads to some deep questions of non-equilibrium statistical mechanics.

- Series
- Combinatorics Seminar
- Time
- Friday, February 6, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Mihai Ciucu – Indiana University and Georgia Tech

The study of random tilings of planar lattice regions goes back to the solution of the dimer model in the 1960's by Kasteleyn, Temperley and Fisher, but received new impetus in the early 1990's, and has since branched out in several directions in the work of Cohn, Kenyon, Okounkov, Sheffield, and others. In this talk, we focus on the interaction of holes in random tilings, a subject inspired by Fisher and Stephenson's 1963 conjecture on the rotational invariance of the monomer-monomer correlation on the square lattice. In earlier work, we showed that the correlation of a finite number of holes on the triangular lattice is given asymptotically by a superposition principle closely paralleling the superposition principle for electrostatic energy. We now take this analogy one step further, by showing that the discrete field determined by considering at each unit triangle the average orientation of the lozenge covering it converges, in the scaling limit, to the electrostatic field. Our proof involves a variety of ingredients, including Laplace's method for the asymptotics of integrals, Newton's divided difference operator, and hypergeometric function identities.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, February 6, 2009 - 15:00 for 2 hours
- Location
- Skiles 269
- Speaker
- Mohammad Ghomi – School of Mathematics, Georgia Tech

<p>(Please note this course runs from 3-5 pm.)</p>

h-Principle consists of a powerful collection of tools developed by Gromov and others to solve underdetermined partial differential equations or relations which arise in differential geometry and topology. In these talks I will describe the Holonomic approximation theorem of Eliashberg-Mishachev, and discuss some of its applications including the sphere eversion theorem of Smale. Further I will discuss the method of convex integration and its application to proving the C^1 isometric embedding theorem of Nash.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, February 9, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Giuseppe Mastroianni – Dept. of Mathematics and Informatics, Univ. of Basilicata, Italy)

In this talk I will show a simple projection method for Fredholm integral equation (FIE) defined on finite intervals and a Nyström method for FIE defined on the real semiaxis. The first method is based the polynomial interpolation of functions in weighted uniform norm. The second one is based on a Gauss truncated quadrature rule. The stability and the convergence of the methods are proved and the error estimates are given.

- Series
- CDSNS Colloquium
- Time
- Monday, February 9, 2009 - 16:30 for 2 hours
- Location
- Skiles 255
- Speaker
- Zhilan Feng – Department of Mathematics, Purdue University

Mathematical models are used to study possible impact of drug treatment of infections with the human immunodeficiency virus type 1 (HIV-1) on the evolution of the pathogen. Treating HIV-infected patients with a combination of several antiretroviral drugs usually contributes to a substantial decline in viral load and an increase in CD4+ T cells. However, continuing viral replication in the presence of drug therapy can lead to the emergence of drug-resistant virus variants, which subsequently results in incomplete viral suppression and a greater risk of disease progression. As different types of drugs (e.g., reverse transcriptase inhibitors,protease inhibitors and entry inhibitors) help to reduce the HIV replication at different stages of the cell infection, infection-age-structured models are useful to more realistically model the effect of these drugs. The model analysis will be presented and the results are linked to the biological questions under investigation. By demonstrating how drug therapy may influence the within host viral fitness we show that while a higher treatment efficacy reduces the fitness of the drug-sensitive virus, it may provide a stronger selection force for drug-resistant viruses which allows for a wider range of resistant strains to invade.

- Series
- Mathematical Finance/Financial Engineering Seminar
- Time
- Tuesday, February 10, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Rehim Kilic – School of Economics, Georgia Tech

This paper introduces a new nonlinear long memory volatility process, denoted by Smooth Transition FIGARCH, or ST-FIGARCH, which is designed to account for both long memory and nonlinear dynamics in the conditional variance process. The nonlinearity is introduced via a logistic transition function which is characterized by a transition parameter and a variable. The model can capture smooth jumps in the altitude of the volatility clusters as well as asymmetric response to negative and positive shocks. A Monte Carlo study finds that the ST-FIGARCH model outperforms the standard FIGARCH model when nonlinearity is present, and performs at least as well without nonlinearity. Applications reported in the paper show both nonlinearity and long memory characterize the conditional volatility in exchange rate and stock returns and therefore presence of nonlinearity may not be the source of long memory found in the data.

- Series
- PDE Seminar
- Time
- Tuesday, February 10, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Quinlan Xia – University of California, Davis

The transportation problem can be formulated as the problem of finding the optimal way to transport a given measure into another with the same mass. In mathematics, there are at least two different but very important types of optimal transportation: Monge-Kantorovich problem and ramified transportation. In this talk, I will give a brief introduction to the theory of ramified optimal transportation. In terms of applied mathematics, optimal transport paths are used to model many "tree shaped" branching structures, which are commonly found in many living and nonliving systems. Trees, river channel networks, blood vessels, lungs, electrical power supply systems, draining and irrigation systems are just some examples. After briefly describing some basic properties (e.g. existence, regularity) as well as numerical simulation of optimal transport paths, I will use this theory to explain the dynamic formation of tree leaves. On the other hand, optimal transport paths provide excellent examples for studying geodesic problems in quasi-metric spaces, where the distance functions satisfied a relaxed triangle inequality: d(x,y) <= K(d(x,z)+d(z,y)). Then, I will introduce a new concept "dimensional distance" on the space of probability measures. With respect to this new metric, the dimension of a probability measure is just the distance of the measure to any atomic measure. In particular, measures concentrated on self-similar fractals (e.g. Cantor set, fat Cantor sets) will be of great interest to us.

- Series
- Research Horizons Seminar
- Time
- Wednesday, February 11, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Wing Suet Li – School of Mathematics, Georgia Tech

The Horn inequalities give a characterization of eigenvalues of self-adjoint n by n matrices A, B, C with A+B+C=0. The original proof by Klyachko and Knutson-Tao, requires tools from algebraic geometry, among other things. Our recent work provides a proof using only elementary tools that made it possible to generalize the Horn inequalities to finite von Neumann factors. No knowledge of von Neumann algebra is required.

- Series
- Analysis Seminar
- Time
- Wednesday, February 11, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Giuseppe Mastroianni – Universita della Basilcata, Potenza, Italy

- Series
- Job Candidate Talk
- Time
- Thursday, February 12, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Ritabrata Munshi – Rutgers University

In late 1980's Manin et al put forward a precise conjecture about the density of rational points on Fano varieties. Over the last two decades some progress has been made towards proving this conjecture. But the conjecture is far from being proved even for the case of two dimensional Fano varieties or del Pezzo surfaces. These surfaces are geometrically classified according to `degree', and the geometric, as well as, the arithmetic complexity increases as the degree drops. The most interesting cases of Manin's conjecture for surfaces are degrees four and lower. In this talk I will mainly focus on the arithmetic of these del Pezzo surfaces, and report some of my own results (partly joint with Henryk Iwaniec). I will also talk about some other problems which apparently have a different flavor but, nonetheless, are directly related with the problem of rational points on surfaces.

- Series
- Stochastics Seminar
- Time
- Thursday, February 12, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Jiawei Liu – Department of Mathematics &amp; Statistics, Georgia State University

If viewed realistically, models under consideration are always false. A consequence of model falseness is that for every data generating mechanism, there exists a sample size at which the model failure will become obvious. There are occasions when one will still want to use a false model, provided that it gives a parsimonious and
powerful description of the generating mechanism. We introduced a model credibility index, from the point of view that the model is false. The model credibility index is defined as the maximum sample size at which samples from the model and those from the true data generating mechanism are nearly indistinguishable. Estimating the model credibility index is under the framework of subsampling, where a large data set is treated as our population, subsamples are generated from the population and compared with the model using various sample sizes. Exploring the asymptotic properties of the model credibility index is associated with the problem of estimating variance of U statistics. An unbiased estimator and a simple fix-up are proposed to estimate the U statistic variance.

- Series
- SIAM Student Seminar
- Time
- Friday, February 13, 2009 - 12:30 for 2 hours
- Location
- Skiles 269
- Speaker
- Yi Huang – School of Mathematics, Georgia Tech

Let V be a vector space over the field C of complex numbers and let GL(V) be the group of isomorphisms of onto itself. Suppose G is a finite group. A linear representation of G in V is a homomorphism from the group G into the group GL(V). In
this talk, I will give a brief introduction to some basic theorems about linear representations of finite groups with concentration on the decomposition of a representation into irreducible sub-representations, and the definition and some nice
properties of the character. At the end of the talk, I will re-prove the Burnside lemma in the group theory from the representation theory approach.
Since I began learning the topic only very recently, hence an absolute novice myself, I invite all of you to the talk to help me learn the knowledge through presenting it to others. If you are familiar with the topic and want to learn something new, my
talk can easily be a disappointment.

- Series
- Probability Working Seminar
- Time
- Friday, February 13, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 268
- Speaker
- Stas Minsker – School of Mathematics, Georgia Tech

This term, the main topic for the Probability Working Seminar will be the coupling method, broadly understood. In the first talk, some basics on coupling will be discussed along with classical examples such as the ergodic theorem for Markov chains.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, February 13, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Igor Belegradek – School of Mathematics, Georgia Tech

Comparison geometry studies Riemannian manifolds with a given curvature bound. This minicourse is an introduction to volume comparison (as developed by Bishop and Gromov), which is fundamental in understanding manifolds with a lower bound on Ricci curvature. Prerequisites are very modest: we only need basics of Riemannian geometry, and fluency with fundamental groups and metric spaces. In the first (2 hour) lecture I shall explain what volume comparison is and derive several applications.

- Series
- Geometry Topology Seminar
- Time
- Monday, February 16, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- John Etnyre – School of Mathematics, Georgia Tech

I will discuss a couple of applications of transverse knot theory to the classification of contact structures and braid theory. In particular I will make the statement "transverse knots classify contact structures" precise and then prove it (if we have time). I will also discuss how progress on two of Orevkov's questions concerning quasi-positive knots that have implications for Hilbert's 16th problem.

- Series
- CDSNS Colloquium
- Time
- Monday, February 16, 2009 - 16:30 for 2 hours
- Location
- Skiles 255
- Speaker
- Jose Amigo – Miguel Hernández University, Spain

Permutation entropy was introduced as a complexity measure of time series. Formally, it replaces the symbol blocks in the definition of Shannon entropy by the so-called ordinal patterns –a digest of the ups-and-downs along a finite orbit in a totally ordered state space. Later, this concept was extended to self maps of n-dimensional intervals, in metric and topological versions. It can be proven that, under some assumptions, the metric and topological permutation entropy coincide with their corresponding conventional counterparts. Besides its use as an entropy estimator, permutation entropy has found some interesting applications. We will talk about the detection of determinism in noisy time series, and the recovery of the control parameter from the symbolic sequences of a unimodal map (which allows to cryptanalize some chaotic ciphers).

- Series
- PDE Seminar
- Time
- Tuesday, February 17, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Andrej Zlatoš – University of Chicago

We study generalized traveling front solutions of reaction-diffusion equations modeling flame propagation in combustible media. Although the case of periodic media has been studied extensively, until very recently little has been known for general disordered media. In this talk we will address questions of existence, uniqueness, and stability of traveling fronts in this framework.

- Series
- Research Horizons Seminar
- Time
- Wednesday, February 18, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Matt Baker – School of Mathematics, Georgia Tech

I will give a modern bijective proof of Kirchhoff's classical theorem relating the number of spanning trees in a graph to the Laplacian matrix of the graph. The proof will highlight some analogies between graph theory and algebraic geometry.

- Series
- ACO Student Seminar
- Time
- Wednesday, February 18, 2009 - 13:30 for 2 hours
- Location
- ISyE Executive Classroom
- Speaker
- Linji Yang – CS, Georgia Tech

In this talk I will give an introduction of the Markov Chain Monte Carlo Method, which uses markov chains to sample interesting combinatorial objects such as proper colorings, independent sets and perfect matchings of a graph. I will introduce methods such as Couplings and Canonical Paths which have been widely used to analyze how many steps Markov Chains needs to go (mixing time) in order to get a sufficiently random combinatorial object. I will also give a brief survey of some recent results in the sampling of colorings.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, February 19, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Amigo Garcia – Miguel Hernández University, Spain

Molecular topology is an application of graph theory to fields like chemistry, biology and pharmacology, in which the molecular structure matters. Its scope is the topological characterization of molecules by means of numerical invariants, called topological indices, which are the main ingredient of the molecular topological models. These models have been instrumental in the discovery of new applications of naturally occurring molecules, as well as in the design of synthetic molecules with specific chemical, biological or pharmacological properties. The talk will focus on pharmacological applications.

- Series
- Graph Theory Seminar
- Time
- Thursday, February 19, 2009 - 12:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Peter Horak – University of Washington, Tacoma

Tiling problems belong to the oldest problems in whole mathematics. They attracted attention of many famous mathematicians. Even one of the Hilbert problems is devoted to the topic. The interest in tilings by unit cubes originated with a conjecture raised by Minkowski in 1908. In this lecture we will discuss the conjecture, and other closely related problems.

- Series
- Stochastics Seminar
- Time
- Thursday, February 19, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Heinrich Matzinger – School of Mathematics, Georgai Tech

We explore the connection between Scenery Reconstruction and Optimal Alignments. We present some new algorithms which work in practise and not just in theory, to solve the Scenery Reconstruction problem

- Series
- SIAM Student Seminar
- Time
- Friday, February 20, 2009 - 12:30 for 2 hours
- Location
- Skiles 269
- Speaker
- Ke Yin – School of Mathematics, Georgia Tech

In this introductory talk, I am going to derive the basic governing equations of fluid dynamics. Our assumption are the three physical principles: the conservation of mass, Newton's second law, and the conservation of energy. The main object is to present Euler equations (which characterize inviscid flow) and Navier-Stokes equations (which characterize viscid flow).

- Series
- Other Talks
- Time
- Friday, February 20, 2009 - 15:00 for 2 hours
- Location
- Skiles 269
- Speaker
- Igor Belegradek – School of Mathematics, Georgia Tech

Comparison geometry studies Riemannian manifolds with a given curvature bound. This minicourse is an introduction to volume comparison (as developed by Bishop and Gromov), which is fundamental in understanding manifolds with a lower bound on Ricci curvature. Prerequisites are very modest: we only need basics of Riemannian geometry, and fluency with fundamental groups and metric spaces. The second (2 hour) lecture is about Gromov-Hausdorff convergence, which provides a natural framework to studying degenerations of Riemannian metrics.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, February 20, 2009 - 15:00 for 2 hours
- Location
- Skiles 269
- Speaker
- Igor Belegradek – Ga Tech

Comparison geometry studies Riemannian manifolds with a given curvature bound. This minicourse is an introduction to volume comparison (as developed by Bishop and Gromov), which is fundamental in understanding manifolds with a lower bound on Ricci curvature. Prerequisites are very modest: we only need basics of Riemannian geometry, and fluency with fundamental groups and metric spaces. The second (2 hour) lecture is about Gromov-Hausdorff convergence, which provides a natural framework to studying degenerations of Riemannian metrics.

- Series
- Combinatorics Seminar
- Time
- Friday, February 20, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Ernie Croot – School of Mathematics, Georgia Tech

In this work (joint with Derrick Hart), we show that there exists a constant c > 0 such that the following holds for all n sufficiently large: if S is a set of n monic polynomials over C[x], and the product set S.S = {fg : f,g in S}; has size at most n^(1+c), then the sumset S+S = {f+g : f,g in S}; has size \Omega(n^2). There is a related result due to Mei-Chu Chang, which says that if S is a set of n complex numbers, and |S.S| < n^(1+c), then |S+S| > n^(2-f(c)), where f(c) -> 0 as c -> 0; but, there currently is no result (other than the one due to myself and Hart) giving a lower bound of the quality >> n^2 for |S+S| for a fixed value of c. Our proof combines combinatorial and algebraic methods.

- Series
- Probability Working Seminar
- Time
- Friday, February 20, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 268
- Speaker
- Sergio Almada – School of Mathematics, Georgia Tech

The talk is based on a paper by Kuksin, Pyatnickiy, and Shirikyan. In this paper, the convergence to a stationary distribution is established by partial coupling. Here, only finitely many coordinates in the (infinite-dimensional) phase space participate in the coupling while the dynamics takes care of the other coordinates.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, February 23, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Tiejun Li – Peking University

The tau-leaping algorithm is proposed by D.T. Gillespie in 2001 for accelerating the simulation for chemical reaction systems. It is faster than the traditional stochastic simulation algorithm (SSA), which is an exact simulation algorithm. In this lecture, I will overview some recent mathematical results on tau-leaping done by our group, which include the rigorous analysis, construction of the new algorithm, and the systematic analysis of the error.

- Series
- Geometry Topology Seminar
- Time
- Monday, February 23, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Stavros Garoufalidis – School of Mathematics, Georgia Tech – stavros@math.gatech.edu

A cubic graph is a graph with all vertices of valency 3. We will show how to assign two numerical invariants to a cubic graph: its spectral radius, and a number field. These invariants appear in asymptotics of classical spin networks, and are notoriously hard to compute. They are known for the Theta graph, the Tetrahedron, but already unknown for the Cube and the K_{3,3} graph. This is joint work with Roland van der Veen: arXiv:0902.3113.

- Series
- Analysis Seminar
- Time
- Monday, February 23, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Eric Rains – Caltech

Euler's beta (and gamma) integral and the associated orthogonal polynomials lie at the core of much of the theory of special functions, and many generalizations have been studied, including multivariate analogues (the Selberg integral; also work of Dixon and Varchenko), q-analogues (Askey-Wilson, Nasrallah-Rahman), and both (work of Milne-Lilly and Gustafson; Macdonald and Koornwinder for orthgonal polynomials). (Among these are the more tractable sums arising in random matrices/tilings/etc.) In 2000, van Diejen and Spiridonov conjectured a further generalization of the Selberg integral, going beyond $q$ to the elliptic level (replacing q by a point on an elliptic curve). I'll discuss two proofs of their conjecture, and the corresponding elliptic analogue of the Macdonald and Koornwinder orthogonal polynomials. In addition, I'll discuss a further generalization of the elliptic Selberg integral with a (partial) symmetry under the exceptional Weyl group E_8, and its relation to Sakai's elliptic Painlev equation.

- Series
- CDSNS Colloquium
- Time
- Monday, February 23, 2009 - 16:30 for 2 hours
- Location
- Skiles 255
- Speaker
- Zhiwu Lin – School of Mathematics, Georgia Tech

A plasma is a completed ionized gas. In many applications such as in nuclear fusion or astrophysical phenomena, the plasma has very high temperature and low density, thus collisions can be ignored. The standard kinetic models for a collisionless plasma are the Vlasov- Maxwell and Vlasov-Poisson systems. The Vlasov-Poisson system is also used to model galaxy dynamics, where a star plays the role of a particle. There exists infinitely many equilibria for Vlasov models and their stability is a very important issue in physics. I will describe some of my works on stability and instability of various Vlasov equilibria.

- Series
- PDE Seminar
- Time
- Tuesday, February 24, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Govind Menon – Brown University

The problem of understanding the parabolic hull of Brownian motion arises in two different fields. In mathematical physics this is the Burgers-Hopf caricature of turbulence (very interesting, even if not entirely turbulent). In statistics, the limit distribution we study was first considered by Chernoff, and forms the cornerstone of a large class of limit theorems that have now come to be called 'cube-root-asymptotics'. It was in the statistical context that the problem was first solved completely in the mid-80s by Groeneboom in a tour de force of hard analysis. We consider another approach to his solution motivated by recent work on stochastic coalescence (especially work of Duchon, Bertoin, and my joint work with Bob Pego). The virtues of this approach are simplicity, generality, and the appearance of a completely unexpected Lax pair. If time permits, I will also indicate some tantalizing links of this approach with random matrices. This work forms part of my student Ravi Srinivasan's dissertation.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, February 25, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Yuriy Mileyko – School of Biology, Georgia Tech

The expression dynamics of interacting genes depends on the topology of the regulatory network, the quantitative nature of feedbacks and interactions between DNA, RNA and proteins, and the biochemical state of the intracellular and surrounding environment. In this talk we show that dynamics of a gene regulatory network can also depend sensitively on the copy number of genes and promoters. Genetic regulatory networks include an overrepresentation of subgraphs commonly known as network motifs. We consider positive feedback, bistable feedback, and toggle switch motifs and show that variation in gene copy number can cause a sequence of saddle-node bifurcations in the corresponding differential equations models, which leads to multiple orders of magnitude change in gene expression. A similar analysis of a 3-gene motif with successive inhibition (the ``repressilator'') reveals that changes in gene copy number can also cause a Hopf bifurcation, thus leading to a qualitative switch in system behavior among oscillatory and equilibrium dynamics. Importantly, we show that these bifurcations exist over a wide range of parameter values, thus reinforcing our claim that copy number is a key control parameter in the expression dynamics of regulatory networks.

- Series
- Research Horizons Seminar
- Time
- Wednesday, February 25, 2009 - 12:00 for 2 hours
- Location
- Skiles 255
- Speaker
- Federico Bonetto – School of Mathematics, Georgia Tech

I'll give a brief introduction to the to Quantum Statistical Mechanics in the case of systems of Fermions (e.g. electrons) and try to show that a lot of the mathematical problems can be framed in term of counting (Feynman) graphs or estimating large determinants.

- Series
- ACO Student Seminar
- Time
- Wednesday, February 25, 2009 - 13:30 for 2 hours
- Location
- Skiles 269
- Speaker
- Daniel Dadush – ISyE, Georgia Tech

In this talk, I will introduce the class of logconcave and s-concave functions, illustrate their properties, and explain their connections to convex geometry. I will present a simple and unified approach for proving probabilistic inequalities for logconcave and s-concave densities on the real line. Lastly I will use these techniques to prove two important theorems in convex geometry: Grunbaum's theorem, every halfspace cut through the centroid of a convex body contains at least a 1/e volume fraction of the body, and the Milman-Pajor inequality, a convex body in R^n is sandwiched between its inertial ellipsoid and a factor n scaling of it. Joint work with Santosh Vempala.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, February 26, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Igor Pak – University of Minnesota

The study of partition identities has a long history going back to Euler, with applications ranging from Analysis to Number Theory, from Enumerative Combina- torics to Probability. Partition bijections is a combinatorial approach which often gives the shortest and the most elegant proofs of these identities. These bijections are then often used to generalize the identities, find "hidden symmetries", etc. In the talk I will present a modern approach to partition bijections based on the geometry of random partitions and complexity ideas.

- Series
- Stochastics Seminar
- Time
- Thursday, February 26, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Henri Matzinger – School of Mathematics, Georgia Tech

Last week we saw combinatorial reconstruction. This time we are going to explain a new approach to Scenery Reconstruction. This new approach could allow us to prove that being able to distinguish sceneries implies reconstructability.

- Series
- SIAM Student Seminar
- Time
- Friday, February 27, 2009 - 12:30 for 2 hours
- Location
- Skiles 269
- Speaker
- Weizhe Zhang – School of Mathematics, Georgia Tech

This talk will follow Peter Lax on the linear algebraic fact of the index of Fredholm operators such as the product formula and stability, all of which are totally elementary.

- Series
- Combinatorics Seminar
- Time
- Friday, February 27, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Benny Sudakov – UCLA

We show that for all \el an \epsilon>0 there is a constant c=c(\ell,\epsilon)>0 such that every \ell-coloring of the triples of an N-element set contains a subset S of size c\sqrt{\log N} such that at least 1-\epsilon fraction of the triples of S have the same color. This result is tight up to the constant c and answers an open question of Erd\H{o}s and Hajnal from 1989 on discrepancy in hypergraphs. For \ell \geq 4 colors, it is known that there is an \ell-coloring of the triples of an N-element set whose largest monochromatic subset has cardinality only \Theta(\log \log N). Thus, our result demonstrates that the maximum almost monochromatic subset that an \ell-coloring of the triples must contain is much larger than the corresponding monochromatic subset. This is in striking contrast with graphs, where these two quantities have the same order of magnitude. To prove our result, we obtain a new upper bound on the \ell-color Ramsey numbers of complete multipartite 3-uniform hypergraphs, which answers another open question of Erd\H{o}s and Hajnal. (This is joint work with D. Conlon and J. Fox.)

- Series
- Other Talks
- Time
- Friday, February 27, 2009 - 15:00 for 2 hours
- Location
- Skiles 269
- Speaker
- Igor Belegradek – School of Mathematics, Georgia Tech

Comparison geometry studies Riemannian manifolds with a given curvature bound. This minicourse is an introduction to volume comparison (as developed by Bishop and Gromov), which is fundamental in understanding manifolds with a lower bound on Ricci curvature. Prerequisites are very modest: we only need basics of Riemannian geometry, and fluency with fundamental groups and metric spaces. In the third (2 hour) lecture I shall prove volume and Laplacian comparison theorems.

- Series
- Probability Working Seminar
- Time
- Friday, February 27, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 268
- Speaker
- Sergio Almada – School of Mathematics, Georgia Tech

This is a continuation of last week's seminar. The talk is based on a paper by Kuksin, Pyatnickiy, and Shirikyan. In this paper, the convergence to a stationary distribution is established by partial coupling. Here, only finitely many coordinates in the (infinite-dimensional) phase space participate in the coupling while the dynamics takes care of the other coordinates.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, February 27, 2009 - 15:05 for 2.5 hours
- Location
- Skiles 269
- Speaker
- Igor Belegradek – Ga Tech

Comparison geometry studies Riemannian manifolds with a given curvature bound. This minicourse is an introduction to volume comparison (as developed by Bishop and Gromov), which is fundamental in understanding manifolds with a lower bound on Ricci curvature. Prerequisites are very modest: we only need basics of Riemannian geometry, and fluency with fundamental groups and metric spaces. In the third (2 hour) lecture I shall prove volume and Laplacian comparison theorems.

- Series
- Geometry Topology Seminar
- Time
- Monday, March 2, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Keiko Kawamuro – IAS

We introduce a construction of an immersed surface for a null-homologous braid in an annulus open book decomposition. This is hinted by the so called Bennequin surface for a braid in R^3. By resolving the singularities of the immersed surface, we obtain an embedded Seifert surface for the braid. Then we compute a self-linking number formula using this embedded surface and observe that the Bennequin inequality is satisfied if and only the contact structure is tight. We also prove that our self-linking formula is invariant (changes by 2) under a positive (negative) braid stabilization which preserves (changes) the transverse knot class.

- Series
- Algebra Seminar
- Time
- Monday, March 2, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Uli Walther – Purdue University

Starting with some classical hypergeometric functions, we explain how to derive their classical univariate differential equations. A severe change of coordinates transforms this ODE into a system of PDE's that has nice geometric aspects. This type of system, called A-hypergeometric, was introduced by Gelfand, Graev, Kapranov and Zelevinsky in about 1985. We explain some basic questions regarding these systems. These are addressed through homology, combinatorics, and toric geometry.

- Series
- PDE Seminar
- Time
- Tuesday, March 3, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Marianne Korten – Kansas State University, Manhattan

In this talk I will describe recent work with C. N. Moore about the two-phase Stefan problem with a degenerate zone. We start with local solutions (no reference to initial or boundary data) and then obtain intrinsic energy estimates, that will in turn lead to the continuity of the temperature. We then show existence and uniqueness of solutions with signed measures as data. The uniqueness problem with signed measure data has been open for some 30 years for any degenerate parabolic equation.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, March 4, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Sean Ellermeyer – Kennesaw State University

We consider a class of age-structured population models in which the central modeling assumption is simply that the birth rate depends on the size of the adult population. For the most part, we in fact assume that the birth rate is a monotone non-decreasing function of the adult population size. Despite the simplicity of our modeling assumptions (or perhaps because of it), we will see that this class of models admits a wide variety of solutions (exponentially growing, lineary growing, periodic, etc.) Much of the analysis of these models can be carried out using elementary techniques and we present some specific examples in which explicit solutions (which are elementary functions) can be generated. We also consider some questions related to the inverse problem for these models.

- Series
- ACO Student Seminar
- Time
- Wednesday, March 4, 2009 - 13:30 for 2 hours
- Location
- ISyE Executive Classroom
- Speaker
- Shiva Kintali – CS, Georgia Tech

Scarf's lemma is one of the fundamental results in combinatorics, originally introduced to study the core of an N-person game. Over the last four decades, the usefulness of Scarf's lemma has been demonstrated in several important combinatorial problems seeking stable solutions. However, the complexity of the computational version of Scarf's lemma (Scarf) remained open. In this talk, I will prove that Scarf is complete for the complexity class PPAD. This shows that Scarf is as hard as the computational versions of Brouwer's fixed point theorem and Sperner's lemma. Hence, there is no polynomial-time algorithm for Scarf unless PPAD \subseteq P. I will also talk about fractional stable paths problem, finding fractional kernels in digraphs, finding fractional stable matching in hypergraphic preference systems and finding core in an N-person balanced game with non-transferable utilities. I will show the connection between these problems through Scarf's lemma and address the complexity of these problems.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, March 5, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Rick Kenyon – Mathematics Department, Brown University

This is joint work with Andrei Okounkov. The ``honeycomb dimer model'' is a natural model of discrete random surfaces in R^3. It is possible to write down a ``Law of Large Numbers" for such surfaces which describes the typical shape of a random surface when the mesh size tends to zero. Surprisingly, one can parameterize these limit shapes in a very simple way using analytic functions, somewhat reminiscent of the Weierstrass parameterization of minimal surfaces. This is even more surprising since the limit shapes tend to be facetted, that is, only piecewise analytic. There is a large family of boundary conditions for which we can obtain exact solutions to the limit shape problem using algebraic geometry techniques. This family includes the (well-known) solution to the limit shape of a ``boxed plane partition'' and has many generalizations.

- Series
- Stochastics Seminar
- Time
- Thursday, March 5, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Yuanhui Xiao – Department of Mathematics and Statistics, Georgia State University

A shot noise process is essentially a compound Poisson process whereby the arriving shots are allowed to accumulate or decay after their arrival via some preset shot (impulse response) function. Shot noise models see applications in diverse areas such as insurance, ﬁ- nance, hydrology, textile engineering, and electronics. This talk stud- ies several statistical inference issues for shot noise processes. Under mild conditions, ergodicity is proven in that process sample paths sat- isfy a strong law of large numbers and central limit theorem. These results have application in storage modeling. Shot function parameter estimation from a data history observed on a discrete-time lattice is then explored. Optimal estimating functions are tractable when the shot function satisﬁes a so-called interval similar condition. Moment methods of estimation are easily applicable if the shot function is com- pactly supported and show good performance. In all cases, asymptotic normality of the proposed estimators is established.

- Series
- SIAM Student Seminar
- Time
- Friday, March 6, 2009 - 12:30 for 2 hours
- Location
- Skiles 269
- Speaker
- Kai Ni – School of Mathematics, Georgia Tech

In this talk, I will briefly introduce some basics of mathematical learning theory. Two basic methods named perceptron algorithm and support vector machine will be explained for the separable classification case. Also, the subgaussian random
variable and Hoeffding inequality will be mentioned in order to provide the upper bound for the deviation of the empirical risk. If time permits, the Vapnik combinatorics will be involved for shaper bounds of this deviation.

- Series
- Probability Working Seminar
- Time
- Friday, March 6, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 268
- Speaker
- Alex Grigo – School of Mathematics, Georgia Tech

The talk is based on the paper titled "Anosov diffeomorphisms and coupling" by Bressaud and Liverani. Existence and uniqueness of SRB invariant measure for the dynamics is established via a coupling of initial conditions introduced to dynamics by L.-S. Young.

- Series
- Combinatorics Seminar
- Time
- Friday, March 6, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Alexey Spiridonov – MIT

This is joint work with Alex Postnikov. Imagine that you are to build a system of space stations (graph vertices), which communicate via laser beams (edges). The edge directions were already chosen, but you must place the stations so that none of the beams miss their targets. In this talk, we let the edge directions be generic and independent, a choice that constrains vertex placement the most. For K_{3} in \mathbb{R}^{2}, the edges specify a unique triangle, but its size is arbitrary --- D_{2}(K_{3})=1 degree of freedom; we say that K_{3} is rigid in \mathbb{R}^{2}. We call D_{n}(G) the degree of parallel rigidity of the graph for generic edge directions. We found an elegant combinatorial characterization of D_{n}(G) --- it is equal to the minimal number of edges in the intersection of n spanning trees of G. In this talk, I will give a linear-algebraic proof of this result, and of some other properties of D_{n}(G). The notion of parallel graph rigidity was previously studied by Whiteley and Develin-Martin-Reiner. The papers worked with the generic parallel rigidity matroid; I will briefly compare our results in terms of D_{n}(G) with the previous work.

- Series
- Geometry Topology Seminar
- Time
- Monday, March 9, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Sinem Onaran – School of Mathematics, Georgia Tech

Given any contact 3-manifold, Etnyre and Ozbagci defined new invariants of the contact structures in terms of open book decompositions supporting the contact structure. One of the invariants is the support genus of the contact structure which is defined as the minimal genus of a page of an open book that supports the contact structure. In a similar fashion, we define the support genus sg(L) of a Legendrian knot L in a contact manifold M as the minimal genus of a page of an open book of M supporting the contact structure such that L sits on a page and the framing given by the contact structure and by the page agree. In this talk, we will discuss the support genus of Legendrian knots in contact 3-manifolds. We will show any null-homologous loose knot has support genus zero. To prove this, we observe an interesting topological property of knots and links on the way. We observe any topological knot or link in a 3-manifold sits on a planar page (genus zero page) of an open book decomposition.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, March 9, 2009 - 13:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Zhi J. Wang – Aerospace Engineering, Iowa State University

The current breakthrough in computational fluid dynamics (CFD) is the emergence of unstructured grid based high-order (order > 2) methods. The leader is arguably the discontinuous Galerkin method, amongst several other methods including the multi-domain spectral, spectral volume (SV), and spectral difference (SD) methods. All these methods possess the following properties: k-exactness on arbitrary grids, and compactness, which is especially important for parallel computing. In this talk, recent progresses in the DG, SV, SD and a unified formulation called lifting collocation penalty will be presented. Numerical simulations with the SV and the SD methods will be presented. The talk will conclude with several remaining challenges in the research on high-order methods.

- Series
- CDSNS Colloquium
- Time
- Monday, March 9, 2009 - 16:30 for 2 hours
- Location
- Skiles 255
- Speaker
- Mark Pollicott – University of Warwick

The Cohen-Gallavotti Fluctuation theorem is a result describing the behaviour of simple hyperbolic dynamical systems. It was introduced to illustrate, in a somewhat simpler context, anomalies in the second law of thermodynamics. I will describe the mathematical formulation of this Fluctuation Theorem, and some variations on it.

- Series
- PDE Seminar
- Time
- Tuesday, March 10, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Hans Knüpfer – Courant Institute, New York

We consider the the following fourth order degenerate parabolic equation h_t + (hh_xxx)_x = 0. The equation arises in the lubrication approximation regime, describing the spreading of a thin film liquid with height profile h >= 0 on a plate. We consider the equation as free boundary problem, defined on its positivity set. We address existence and regularity of classical solutions in weighted Hölder and Sobolev spaces.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, March 11, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Dirk Brockmann – Northwestern University

Human Mobility in our globalised world has reached a complexity and volume of unprecedented degree. More than 60 million people travel billions of kilometres on more than 2 million international flights each week. Hundreds of millions of people commute on a complex web of highways and railroads most of which operate at their maximum capacity. Human mobility is responsible for the geographical spread of emergent human infectious diseases and plays a key role in human mediated bioinvasion, the dominant factor in the global biodiversity crisis. I will report on the recent discovery of scaling laws in global human traffic (obtained from online bill-tracking at www.wheresgeorge.com) and mathematical models that can account for it. I will present a complex network perspective on multi-scale human traffic networks, report on their statistical properties and show that they can be used to identify geographically coherent communities that only vaguely resemble administrative ones. The approach provides an operational segmentation of maps into a hierarchical set of effective regions and boundaries based on human behavior. I will briefly talk about European transportation networks, geocaching and trackable items.

- Series
- Combinatorics Seminar
- Time
- Wednesday, March 11, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Ann Trenk – Department of Mathematics, Wellesley College

Tolerance graphs were introduced in 1982 by Golumbic and Monma as a generalization of the class of interval graphs. A graph G= (V, E) is an interval graph if each vertex v \in V can be assigned a real interval I_v so that xy \in E(G) iff I_x \cap I_y \neq \emptyset. Interval graphs are important both because they arise in a variety of applications and also because some well-known recognition problems that are NP-complete for general graphs can be solved in polynomial time when restricted to the class of interval graphs. In certain applications it can be useful to allow a representation of a graph using real intervals in which there can be some overlap between the intervals assigned to non-adjacent vertices. This motivates the following definition: a graph G= (V, E) is a tolerance graph if each vertex v \in V can be assigned a real interval I_v and a positive tolerance t_v \in {\bf R} so that xy \in E(G) iff |I_x \cap I_y| \ge \min\{t_x,t_y\}. These topics can also be studied from the perspective of ordered sets, giving rise to the classes of Interval Orders and Tolerance Orders. In this talk we give an overview of work done in tolerance graphs and orders . We use hierarchy diagrams and geometric arguments as unifying themes.

- Series
- Research Horizons Seminar
- Time
- Wednesday, March 11, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Hao Min Zhou – School of Mathematics, Georgia Tech

In this talk, I will present an brief introdution to use partial differential equation (PDE) and variational techniques (including techniques developed in computational fluid dynamics (CFD)) into wavelet transforms and Applications in Image Processing. Two different approaches are used as examples. One is PDE and variational frameworks for image reconstruction. The other one is an adaptive ENO wavelet transform designed by using ideas from Essentially Non-Oscillatory (ENO) schemes for numerical shock capturing.

- Series
- ACO Seminar
- Time
- Wednesday, March 11, 2009 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Klaus 2100
- Speaker
- Nikhil Devanur – Microsoft Research

We consider the problem of a search engine trying to assign a sequence of search keywords to a set of competing bidders, each with a daily spending limit. The goal is to maximize the revenue generated by these keyword sales, bearing in mind that, as some bidders may eventually exceed their budget, not all keywords should be sold to the highest bidder. We assume that the sequence of keywords (or equivalently, of bids) is revealed on-line. Our concern will be the competitive ratio for this problem versus the off-line optimum.
We extend the current literature on this problem by considering the setting where the keywords arrive in a random order. In this setting we are able to achieve a competitive ratio of 1-\epsilon under some mild, but necessary, assumptions. In contrast, it is already known that when the keywords arrive in an adversarial order, the best competitive ratio is bounded away from 1. Our algorithm is motivated by PAC learning, and proceeds in two parts: a training phase, and an exploitation phase.
Joint work with Tom Hayes, UNM.

- Series
- CDSNS Colloquium
- Time
- Thursday, March 12, 2009 - 11:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 269
- Speaker
- Ian F. Putnam – U. Victoria, BC, Canada

Motivated by Smale's work on smooth dynamical systems, David Ruelle introduced the notion of Smale spaces. These are topological dynamical systems which are hyperbolic in the sense of having local coordinates of contracting and expending directions. These include hyperbolic automorphisms of tori, but typically, the spaces involved have a fractal nature. An important subclass are the shifts of finite type which are symbolic systems described by combinatorial data. These are also precisely the Smale spaces which are totally disconnected. Rufus Bowen showed that every Smale space is the image of shift of finite type under a finite-to-one factor map. In the 1970's, Wolfgang Krieger introduced a beautiful invariant for shifts of finite type. The aim of this talk is to show how a refined version of Bowen's theorem may be used to extend Krieger's invariant to all (irreducible) Smale spaces. The talk will assume no prior knowledge of these topics - we begin with a discussion of Smale spaces and shifts of finite type and then move on to Krieger's invariant and its extension.

- Series
- Stochastics Seminar
- Time
- Thursday, March 12, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Hayrie Ayhan – ISyE, Georgia Tech

We consider Markovian tandem queues with finite intermediate buffers and flexible servers and study how the servers should be assigned dynamically to stations in order to obtain optimal long-run average throughput. We assume that each server can work on only one job at a time, that several servers can work together on a single job, and that the travel times between stations are negligible. Under various server collaboration schemes, we characterize the optimal server assignment policy for these systems.

- Series
- CDSNS Colloquium
- Time
- Friday, March 13, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- George Sell – University of Minnesota

The current theory of global attractors for the Navier-Stokes equations on thin 3D domains is motivated by the desire to better understand the theory of heat transfer in the oceans of the Earth. (In this context, the thinness refers to the aspect ratio - depth divided by expanse - of the oceans.) The issue of heat transfer is, of course, closely connected with many of the major questions concerning the climate. In order to exploit the tools of modern dynamical systems in this study, one needs to know that the global attractors are "good" in the sense that the nonlinearities are Frechet differentiable on these attractors. About 20 years ago, it was discovered that on certain thin 3D domains, the Navier-Stokes equations did possess good global attractors. This discovery, which was itself a major milestone in the study of the 3D Navier-Stokes equations, left open the matter of extending the theory to cover oceanic-like regions with the appropriate physical boundary behavior. In this lecture, we will review this theory, and the connections with climate modeling, while placing special emphasis on the recent developments for fluid flows with the Navier (or slip) boundary conditions

- Series
- PDE Seminar
- Time
- Friday, March 13, 2009 - 16:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Eitan Tadmor – University of Maryland, College Park

We discuss the global regularity vs. finite time breakdown in Eulerian dynamics, driven by different models of nonlinear forcing. Finite time breakdown depends on whether the initial configuration crosses intrinsic, O(1) critical thresholds (CT). Our approach is based on spectral dynamics, tracing the eigenvalues of the velocity gradient which determine the boundaries of CT surfaces in configuration space. We demonstrate this critical threshold phenomena with several n-dimensional prototype models. For n=2 we show that when rotational forcing dominates the pressure, it prolongs the life-span of sub-critical 2D shallow-water solutions. We present a stability theory for vanishing viscosity solutions of the 2D nonlinear "pressureless" convection. We revisit the 3D restricted Euler and Euler-Poisson equations, and obtain a surprising global existence result for a large set of sub-critical initial data in the 4D case.

- Series
- Graph Theory Seminar
- Time
- Thursday, March 19, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Sergey Norin – Princeton University

Many results in asymptotic extremal combinatorics are obtained using just a handful of instruments, such as induction and Cauchy-Schwarz inequality. The ingenuity lies in combining these tools in just the right way. Recently,
Razborov developed a flag calculus which captures many of the available techniques in pure form, and allows one, in particular, to computerize the search for the right combination. In this talk we outline the general approach and describe its application to the conjecture that a digraph with minimum outdegree n/3 contains a directed triangle. This special case of the Caccetta-Haggkvist conjecture has been extensively investigated in the past. We show that a digraph with minimum outdegree a*n contains a directed triangle for a = 0.3465. The proof builds on arguments used to establish previously known bounds, due to Shen from 1998 (a = 0.3542) and Hamburger, Haxell and Kostochka from 2008 (a = 0.3531). It consists of a combination of ~80 computer generated inequalities. Based on joint work with Jan Hladky and Daniel Kral.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, March 23, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Shigui Ruan – University of Miami

Understanding the seasonal/periodic reoccurrence of influenza will be very helpful in designing successful vaccine programs and introducing public health interventions. However, the reasons for seasonal/periodic influenza epidemics are still not clear even though various explanations have been proposed. In this talk, we present an age-structured type evolutionary epidemiological model of influenza A drift, in which the susceptible class is continually replenished because the pathogen changes genetically and immunologically from one epidemic to the next, causing previously immune hosts to become susceptible. Applying our recent established center manifold theory for semilinear equations with non-dense domain, we show that Hopf bifurcation occurs in the model. This demonstrates that the age-structured type evolutionary epidemiological model of influenza A drift has an intrinsic tendency to oscillate due to the evolutionary and/or immunological changes of the influenza viruses. (based on joint work with Pierre Magal).

- Series
- ACO Seminar
- Time
- Monday, March 23, 2009 - 16:30 for 2 hours
- Location
- Skiles 269
- Speaker
- Andrea Montanari – Stanford University

Low-rank models are frequently used in machine learning and statistics. An important domain of application is provided by collaborative filtering, whereby a low-rank matrix describes the ratings that a large set of users attribute to a large set of products. The problem is in this case to predict future ratings from a sparse subset currently available. The dataset released for the Netflix challenge provides an ideal testbed for theory and algorithms for learning low-rank matrices. Given M, a random n x n matrix of rank r, we assume that a uniformly random subset E of its entries is observed. We describe an efficient procedure that reconstructs M from |E| = O(rn) observed entries with arbitrarily small root mean square error, whenever M is satisfies an appropriate incoherence condition. If r = O(1), the algorithm reconstructs M exactly from O(n log n) entries. This settles a recent open problem by Candes and Recht. In the process of proving these statements, we obtain a generalization of a celebrated result by Friedman-Kahn-Szemeredi and Feige-Ofek on the spectrum of sparse random matrices. [Based on joint work with R. H. Keshavan and S. Oh]

- Series
- CDSNS Colloquium
- Time
- Monday, March 23, 2009 - 16:30 for 2 hours
- Location
- Skiles 255
- Speaker
- Xiangdong Ye – University of Science and Technology of China

In this talk we will review results on local entropy theory for the past 15 years, introduce the current development and post some open questions for the further study.

- Series
- PDE Seminar
- Time
- Tuesday, March 24, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Thomas Sideris – University of California, Santa Barbara

We will give an overview of results on the global existence of solutions to the initial value problem for nonlinear elastic and viscoelastic materials in 3d without boundary. Materials will be assumed to be isotropic, but both compressible and incompressible cases will be discussed. In the compressible case, a key null condition must be imposed to control nonlinear interactions of pressure waves. This necessary assumption is consistent with the physical model. Initial conditions are small perturbations of a stress free reference state. Existence is proven using a fixed point argument which combines energy estimates and with some new dispersive estimates.

- Series
- Other Talks
- Time
- Tuesday, March 24, 2009 - 17:30 for 2 hours
- Location
- LeCraw Auditorium, Room 100
- Speaker
- Roger Penrose – Mathematical Institute, University of Oxford

There is much impressive observational evidence, mainly from the cosmic microwave background (CMB), for an enormously hot and dense early stage of the universe --- referred to as the Big Bang. Observations of the CMB are now very detailed, but this very detail presents new puzzles of various kinds, one of the most blatant being an apparent paradox in relation to the second law of thermodynamics. The hypothesis of inflationary cosmology has long been argued to explain away some of these puzzles, but it does not resolve some key issues, including that raised by the second law. In this talk, I describe a quite different proposal, which posits a succession of universe aeons prior to our own. The expansion of the universe never reverses in this scheme, but the space-time geometry is nevertheless made consistent through a novel geometrical conception. Some very recent analysis of the CMB data, obtained with the WMAP satellite, will be described, this having a profound but tantalizing bearing on these issues.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, March 25, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Ruslan Rafikov – Medical College of Georgia

The stress condition calls for an adequate activity of key enzymatic systems of cellular defense. Massive protein destabilization and degradation is occurring in stressed cells. The rate of protein re-synthesis (DNA->RNA->protein) is inadequate to adapt to rapidly changing environment. Therefore, an alternative mechanism should exist maintaining sufficient activity of defense enzymes. Interestingly, more than 50% of enzymes consist of identical subunits which are forming multimeric interface. Stabilization of multimers is important for enzymatic activity. We found that it can be achieved by the formation of inter-subunit covalent bridges in response to stress conditions. It shows an elegance of the structure design that directs selective subunits linkage and increases enzyme's robustness and chances of cell survival during the stress. In contrast, modification of aminoacids involved in linkage leads to protein destabilization, unfolding and degradation. These results describe a new instantaneous mechanism of structural adaptation that controls enzymatic system under stress condition.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Wednesday, March 25, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Junping Wang – NSF

This talk will first review domain decomposition methods for second order elliptic equations, which should be accessible to graduate students. The second part of the talk will deal with possible extensions to the Stokes equation when discretized by finite element methods. In particular, we shall point out the difficulties in such a generalization, and then discuss ways to overcome the difficulties.

- Series
- ACO Student Seminar
- Time
- Wednesday, March 25, 2009 - 13:30 for 2 hours
- Location
- ISyE Executive Classroom
- Speaker
- Dana Randall – Computer Science, Georgia Tech

We will survey some old, some new, and some open problems in the area of efficient sampling. We will focus on sampling combinatorial structures (such as perfect matchings and independent sets) on regular lattices. These problems arise in statistical physics, where sampling objects on lattices can be used to determine many thermodynamic properties of simple physical systems. For example, perfect matchings on the Cartesian lattice, more commonly referred to as domino tilings of the chessboard, correspond to systems of diatomic molecules. But most importantly they are just cool problems with some beautiful solutions and a surprising number of unsolved challenges!

- Series
- Other Talks
- Time
- Wednesday, March 25, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Howey Physics Lecture Room 5
- Speaker
- Roger Penrose – Mathematical Institute, University of Oxford

Twistor theory is now over 45 years old. In December 1963, I proposed the initial ideas of this scheme, based on complex-number geometry, which presents an alternative perspective to that of standard 4-dimensional space-time, for the basic arena in which (quantum) physics takes place. Over the succeeding years, there were numerous intriguing developments. But many of these were primarily mathematical, and there was little interest expressed by the physics community. Things changed rather dramatically, in December 2003, when E. Witten produced a 99-page article initiating the subject of “twistor-string theory” this providing a novel approach to high-energy scattering processes. In this talk, I shall provide an account of the original geometrical and physical ideas, and also outline various recent developments, some of which may help our understandings of the seeming paradoxes of quantum mechanics.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, March 26, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Walter Craig – McMaster University

A new estimate on weak solutions of the Navier-Stokes equations in three dimensions gives some information about the partial regularity of solutions. In particular, if energy concentration takes place, the dimension of the microlocal singular set cannot be too small. This estimate has a dynamical systems proof. These results are joint work with M. Arnold and A. Biryuk.

- Series
- SIAM Student Seminar
- Time
- Friday, March 27, 2009 - 12:30 for 2 hours
- Location
- Skiles 255
- Speaker
- Huy Huynh – School of Mathematics, Georgia Tech

This is due to the paper of Dr. Christian Houdre and Trevis Litherland. Let X_1, X_2,..., X_n be a sequence of iid random variables drawn uniformly from a finite ordered alphabets (a_1,...,a_m) where a_1 < a_2 < ...< a_m. Let LI_n be the length of the longest increasing subsequence of X_1,X_2,...,X_n. We'll express the limit distribution of LI_n as functionals of (m-1)-dimensional Brownian motion. This is an elementary case taken from this paper.

- Series
- Combinatorics Seminar
- Time
- Friday, March 27, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Graeme Kemkes – UCSD

Choose a graph uniformly at random from all d-regular graphs on n vertices. We determine the chromatic number of the graph for about half of all values of d, asymptotically almost surely (a.a.s.) as n grows large. Letting k be the smallest integer satisfying d < 2(k-1)\log(k-1), we show that a random d-regular graph is k-colorable a.a.s. Together with previous results of Molloy and Reed, this establishes the chromatic number as a.a.s. k-1 or k. If furthermore d>(2k-3)\log(k-1) then the chromatic number is a.a.s. k. This is an improvement upon results recently announced by Achlioptas and Moore. The method used is "small subgraph conditioning'' of Robinson and Wormald, applied to count colorings where all color classes have the same size. It is the first rigorously proved result about the chromatic number of random graphs that was proved by small subgraph conditioning. This is joint work with Xavier Perez-Gimenez and Nick Wormald.

- Series
- Probability Working Seminar
- Time
- Friday, March 27, 2009 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 268
- Speaker
- Ricardo Restrepo – School of Mathematics, Georgia Tech

This talk is based in the article titled "On the convergence to equilibrium of Kac’s random walk on matrices" by Roberto Oliveira (IMPA, Brazil). We show how a strategy related to the path coupling method allows us to establish tight bounds for the L-2 transportation-cost mixing time of the Kac's random walk on SO(n).

- Series
- Geometry Topology Seminar
- Time
- Monday, March 30, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Yo'av Rieck – University of Arkansas

Let M be a hyperbolic 3-manifold, that is, a 3-manifold admitting a complete, finite volume Riemannian metric of constant section curvature -1. Let S be a Heegaard surface in M, that is, M cut open along S consists of two handlebodies. Our goal is to prove that is the volume of M (denoted Vol(M)) if small than S is simple. To that end we define two complexities for Heegaard surfaces. The first is the genus of the surface (denoted g(S)) and the second is the distance of the surface, as defined by Hempel (denoted d(S)). We prove that there exists a constant K>0 so that for a generic manifold M, if g(S) \geq 76KVol(M) + 26, then d(S) \leq 2. Thus we see that for a generic manifold of small volume, either the genus of S is small or its distance is at most two. The term generic will be explained in the talk.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, March 30, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Richardo March – Istituto per le Applicazioni del Calcolo &quot;Mauro Picone&quot; of C.N.R.

We consider ordered sequences of digital images. At a given pixel a time course is observed which is related to the time courses at neighbour pixels. Useful information can be extracted from a set of such observations by classifying pixels in groups, according to some features of interest. We assume to observe a noisy version of a positive function depending on space and time, which is parameterized by a vector of unknown functions (depending on space) with discontinuities which separate regions with different features in the image domain. We propose a variational method which allows to estimate the parameter functions, to segment the image domain in regions, and to assign to each region a label according to the values that the parameters assume on the region. Approximation by \Gamma-convergence is used to design a numerical scheme. Numerical results are reported for a dynamic Magnetic Resonance imaging problem.

- Series
- Analysis Seminar
- Time
- Monday, March 30, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Jeff Geronimo – School of Mathematics, Georgia Tech

The contracted asymptotics for orthogonal polynomials whose recurrence coefficients tend to infinity will be discussed. The connection between the equilibrium measure for potential problems with external fields will be
exhibited. Applications will be presented which include the Wilson polynomials.

- Series
- CDSNS Colloquium
- Time
- Monday, March 30, 2009 - 16:30 for 2 hours
- Location
- Skiles 255
- Speaker
- Ton Dieker – ISyE, Georgia Tech

Allocation of service capacity ('staffing') at stations in queueing networks is both of fundamental and practical interest. Unfortunately, the problem is mathematically intractable in general and one therefore typically resorts to approximations or computer simulation. This talk describes work in progress with M. Squillante and S. Ghosh (IBM Research) on an algorithm that serves as an approximation for the 'best' capacity allocation rule. The algorithm can be interpreted as a discrete-time dynamical system, and we are interested in uniqueness of a fixed point and in convergence properties. No prior knowledge on queueing networks will be assumed.

- Series
- PDE Seminar
- Time
- Tuesday, March 31, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Kris Jenssen – Penn State University, College Station

We study the problem of constructing systems of hyperbolic conservation laws with prescribed eigencurves, i.e. the eigenvector fields of the Jacobian of the flux are given. We formulate this as a (typically overdetermined) system of equations for the eigenvalues-to-be. Equivalent formulations in terms of differential and algebraic-differential equations are considered. The resulting equations are then analyzed with techniques from exterior differential systems (Cartan-Kahler theory). The cases of 2x2- and 3x3-systems can be treated in detail, and explicit examples show that already the 3x3-case is fairly complex. We also analyze general rich systems. We also characterize conservative systems with the same eigencurves as compressible gas dynamics. This is joint work with Irina Kogan (North Carolina State University).

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, April 1, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Klas Udekwu – Emory University

The treatment of bacterial infections with antibiotics is universally accepted as one of (if not THE) most significant contributions of medical intervention to reducing mortality and morbidity during last century. Despite their widespread use over this extended period however, basic knowledge about how antibiotics kill or prevent the growth of bacteria is only just beginning to emerge. The dose and term of antibiotic treatment has long been determined empirically and intuitively by clinicians. Only recently have antibiotic treatment protocols come under scrutiny with the aim to theoretically and experimentally rationalize treatment protocols. The aim of such scrutiny is to design protocols which maximize antibiotics’ efficacy in clearing bacterial infections and simultaneously prevent the emergence of resistance in treated patients. Central to these endeavors are the pharmacodynamics, PD (relationship between bug and drug), and the pharmacokinetics, PK (the change antibiotic concentration with time) of each bacteria : drug : host combination. The estimation of PD and PK parameters is well established and standardized worldwide and although different PK parameters are commonly employed for most of these considerations, a single PD parameter is usually used, the minimum inhibitory concentration (MIC). MICs, also utilized as the criteria for resistance are determined under conditions that are optimal to the action of the antibiotic; low densities of bacteria growing exponentially. The method for estimating MICs which is the only one officially sanctioned by the regulatory authority (Clinical and Laboratory Standards Institute) defines conditions that rarely obtain outside of the laboratory and virtually never in the bacteria infecting mammalian hosts. Real infections with clinical symptoms commonly involve very high densities of bacteria, most of which are not replicating. These populations are rarely planktonic but rather reside as colonies or within matrices called biofilms which sometimes include other species of bacteria.
In the first part of my talk, I will present newly published data that describes the pharmacodynamic relationship between the sometimes pathogenic bacterium Staphylococcus aureus and antibiotics of six classes and the effects of cell density on MICs. By including density dependent MIC in a standard mathematical model of antibiotic treatment (from our lab), I show that this density-dependence may explain why antibiotic treatment fails in the absence of inherited resistance. In the second part of my talk I will consider the effects of the physiological state of clinical isolates of S. aureus on their susceptibility to different antibiotics. I present preliminary data which suggests that the duration of an infection may contribute adversely to an antibiotics chance of clearing the infection. I conclude with a brief discussion of the implications of the theoretical and experimental results for the development of antibiotic treatment protocols. As a special treat, I will outline problems of antibiotic treatment that could well be addressed with some classy mathematics.

- Series
- ACO Colloquium
- Time
- Wednesday, April 1, 2009 - 16:30 for 2 hours
- Location
- Klaus 1116E
- Speaker
- Ilan Adler – UC Berkeley

One of the most interesting aspects of the Linear Complementarity Problem (LCP) is its range from relatively easy problems such as linear and convex quadratic programming problems to NP-hard problems. A major effort in LCP theory had been the study of the Lemke algorithm, a simplex-like algorithm which is guaranteed to terminate in finite number of iterations but not necessarily with a solution (or a certificate that no solution exists). Over the years, many subclasses of LCP were proven to be workable by the Lemke algorithm. Those subclasses were often characterized as ‘nice’ even when no polynomial upper bound for the algorithm was known to exist. In fact, for most of these classes, instances with exponential number of steps had been discovered. In this talk, I’ll discuss the close connection between these classes and the PPAD (Polynomial-time Parity Argument Directed) complexity class. The discovery that computing Nash equilibrium (which is an LCP) is PPAD complete is particularly significant in analyzing the complexity of LCP. I’ll also discuss the LCP reduction-via-perturbation technique and its relation to the PPAD class and the Lemke Algorithm.
This talk is based on a joint work with Sushil Verma.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, April 2, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Marshall Slemrod – Department of Mathematics, University of Wisconsin

In this talk I will outline recent results of G-Q Chen, Dehua Wang, and me on the problem of isometric embedding a two dimensional Riemannian manifold with negative Gauss curvature into three dimensional Euclidean space. Remarkably there is very pretty duality between this problem and the equations of steady 2-D gas dynamics. Compensated compactness (L.Tartar and F.Murat) yields proof of existence of solutions to an initial value problem when the prescribed metric is the one associated with the catenoid.

- Series
- ACO Student Seminar
- Time
- Thursday, April 2, 2009 - 13:30 for 2 hours
- Location
- Skiles 255
- Speaker
- Alexandra Kolla – UC Berkeley

In the first part of the talk, I am going to give an introduction and overview of linear and semidefinite programming hierarchies. I will mostly review known integrality gaps for such programs and try to give an intuition of why we currently lack strong techniques for designing rounding algorithms. In the second part of the talk I will focus on the stronger SDP Lasserre hierarchy. In contrast with the previous LP and SDP hierarchies, very few examples of integrality gap instances are known to date. I will present a recent technique for designing such instances and discuss open problems in the area.

- Series
- SIAM Student Seminar
- Time
- Friday, April 3, 2009 - 12:30 for 2 hours
- Location
- Skiles 269
- Speaker
- Sergio Almada – School of Mathematics, Georgia Tech

Suppose b is a vector field in R^n such that b(0) = 0. Let A = Jb(0) the Jacobian matrix of b at 0. Suppose that A has no zero eigenvalues, at least one positive and at least one negative eigenvalue. I will study the behavior of the stochastic differential equation dX_\epsilon = b(X_\epsilon) + \epsilon dW as \epsilon goes to 0. I will illustrate the techniques done to deal with this kind of equation and make remarks on how the solution behaves as compared to the deterministic case.

- Series
- Combinatorics Seminar
- Time
- Friday, April 3, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Alexandra Kolla – UC Berkeley

I will present an approximation algorithm for the following problem: Given a graph G and a parameter k, find k edges to add to G as to maximize its algebraic connectivity. This problem is known to be NP-hard and prior to this work no algorithm was known with provable approximation guarantee. The algorithm uses a novel way of sparsifying (patching) part of a graph using few edges.

- Series
- Geometry Topology Seminar
- Time
- Monday, April 6, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Emory, W306 MSC (Math and Science Center)
- Speaker
- John Etnyre – School of Mathematics, Georgia Tech

Joint meeting at Emory

Recall that an open book decomposition of a 3-manifold M is a link L in M whose complement fibers over the circle with fiber a Seifert surface for L. Giroux's correspondence relates open book decompositions of a manifold M to contact structures on M. This correspondence has been fundamental to our understanding of contact geometry. An intriguing question raised by this correspondence is how geometric properties of a contact structure are reflected in the monodromy map describing the open book decomposition. In this talk I will show that there are several interesting monoids in the mapping class group that are related to various properties of a contact structure (like being Stein fillable, weakly fillable, . . .). I will also show that there are open book decompositions of Stein fillable contact structures whose monodromy cannot be factored as a product of positive Dehn twists. This is joint work with Jeremy Van Horn-Morris and Ken Baker.

- Series
- Geometry Topology Seminar
- Time
- Monday, April 6, 2009 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Emory, W306 MSC (Math and Science Center)
- Speaker
- Noel Brady – University of Oklahoma

Joint meeting at Emory

A k--dimensional Dehn function of a group gives bounds on the volumes of (k+1)-balls which fill k--spheres in a geometric model for the group. For example, the 1-dimensional Dehn function of the group Z^2 is quadratic. This corresponds to the fact that loops in the euclidean plane R^2 (which is a geometric model for Z^2) have quadratic area disk fillings. In this talk we will consider the countable sets IP^{(k)} of numbers a for which x^a is a k-dimensional Dehn function of some group. The situation k \geq 2 is very different from the case k=1.

- Series
- CDSNS Colloquium
- Time
- Monday, April 6, 2009 - 16:30 for 2 hours
- Location
- Skiles 255
- Speaker
- Vera Mikyoung Hur – MIT

I will speak on the dispersive character of waves on the interface between vacuum and water under the influence of gravity and surface tension. I will begin by giving a precise account of the formulation of the surface water-wave problem and discussion of its distinct features. They include the dispersion relation, its severe nonlinearity, traveling waves and the Hamiltonian structure. I will describe the recent work of Hans Christianson, Gigliola Staffilani and myself on the local smoothing effect of 1/4 derivative for the fully nonlinear problem under surface tension with some detail of the proof. If time permits, I will explore some open questions regarding long-time behavior and stability.

- Series
- Combinatorics Seminar
- Time
- Tuesday, April 7, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Adam Marcus – Yale University

The entropy function has a number of nice properties that make it a useful
counting tool, especially when one wants to bound a set with respect to the set's
projections. In this talk, I will show a method developed by Mokshay Madiman, Prasad
Tetali, and myself that builds on the work of Gyarmati, Matolcsi and Ruzsa as well as
the work of Ballister and Bollobas. The goal will be to give a black-box method for
generating projection bounds and to show some applications by giving new bounds on
the sizes of Abelian and non-Abelian sumsets.

- Series
- PDE Seminar
- Time
- Tuesday, April 7, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Joseph Jerome – Northwestern University, Evanston

The Cauchy problem for the Poisson-Nernst-Planck/Navier-Stokes model was investigated by the speaker in [Transport Theory Statist. Phys. 31 (2002), 333-366], where a local existence-uniqueness theory was demonstrated, based upon Kato's framework for examining evolution equations. In this talk, the existence of a global distribution solution is proved to hold for the model, in the case of the initial-boundary value problem. Connection of the above analysis to significant applications is discussed. The solution obtained is quite rudimentary, and further progress would be expected in resolving issues of regularity.

- Series
- Analysis Seminar
- Time
- Tuesday, April 7, 2009 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Andrei Kapaev – Indiana University-Purdue University Indianapolis

Solutions of the simplest of the Painleve equations, PI, y'' = 6y^2+x, exhibit surprisingly rich asymptotic properties as x is large. Using the Riemann-Hilbert problem approach, we find an exponentially small addition to an algebraically large background admitting a power series asymptotic expansion and explain how this "beyond of all orders" term helps us to compute the coefficient asymptotics in the preceding series.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, April 8, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Shandelle Henson – Andrews University

Oscillator synchrony can occur through environmental forcing or as a phenomenon of spontaneous self-organization in which interacting oscillators adjust phase or period and begin to cycle together. Examples of spontaneous synchrony have been documented in a wide variety of electrical, mechanical, chemical, and biological systems, including the menstrual cycles of women. Many colonial birds breed approximately synchronously within a time window set by photoperiod. Some studies have suggested that heightened social stimulation in denser colonies can lead to a tightened annual reproductive pulse (the “Fraser Darling effect”). It has been unknown, however, whether avian ovulation cycles can synchronize on a daily timescale within the annual breeding pulse. We will discuss socially-stimulated egg-laying synchrony in a breeding colony of glaucous-winged gulls using Monte Carlo analysis and a discrete-time dynamical system model.

- Series
- Research Horizons Seminar
- Time
- Wednesday, April 8, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Hao Min Zhou – School of Mathematics, Georgia Tech

This talk will be a continuation of the one I gave in this Seminar on March~11. I will present a brief introduction to use partial differential equations (PDE) and variational techniques (including techniques developed in computational fluid dynamics (CFD)) into wavelet transforms and Applications in Image Processing. Two different approaches are used as examples. One is PDE and variational frameworks for image reconstruction. The other one is an adaptive ENO wavelet transform designed by using ideas from Essentially Non-Oscillatory (ENO) schemes for numerical shock capturing.

- Series
- ACO Student Seminar
- Time
- Wednesday, April 8, 2009 - 13:30 for 2 hours
- Location
- ISyE Executive Classroom
- Speaker
- Jean Bellissard – Schools of Mathematics and Physics, Georgia Tech

This short introduction to the principles of Quantum Computation will give hints upon why quantum computers, if they are built, will revolutionize the realm of information technology. If Physicists and Engineers can produce such machines, all the security protocoles used today will become obsolete and complex computations called NP will become easy. From the example of trapped ion computation, the talk will explain how Quantum Mechanics helps encoding information. The notion of quantum gate, the elementary brick of computation, will be introduced and some example of elementary program will be described. Comments about the Fourier transformalgorithm, its potential speed and its application to code breaking will end this talk.

- Series
- Dissertation Defense
- Time
- Wednesday, April 8, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Hwa Kil Kim – School of Mathematics, Georgia Tech

- Series
- Stochastics Seminar
- Time
- Thursday, April 9, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Elton Hsu – Department of Mathematics, Northwestern University

The Cameron-Martin theorem is one of the cornerstones of stochastic analysis. It asserts that the shifts of the Wiener measure along certain flows are equivalent. Driver and others have shown that this theorem, after an appropriate reformulation, can be extension to the Wiener measure on the path space over a compact Riemannian manifold. In this talk we will discuss this and other extensions of the Cameron-Martin theorem and show that it in fact holds for an arbitrary complete Riemannian manifold.

- Series
- SIAM Student Seminar
- Time
- Friday, April 10, 2009 - 12:30 for 2 hours
- Location
- Skiles 269
- Speaker
- Tianjun Ye – School of Mathematics, Georgia Tech

Linear algebra method is a very useful method in combinatorics. Lovas Theorem (a very deep theorem about perfect graph) is proved by using this way. The idea is, if we want to come up with an upper bound on the size of a set of objects, associate them with elements in a vector space V of relatively low dimension, and show that these
elements are linearly independent. Then we cannot have more objects in our set than the dimension of V. We will show we can use this way to solve some combinatorics problem, such as odd town problem and two-distance sets problem.

- Series
- ACO Seminar
- Time
- Friday, April 10, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Saugata Basu – School of Mathematics, Georgia Tech and Purdue University

Toda proved in 1989 that the (discrete) polynomial time hierarchy, {\bf PH}, is contained in the class {\bf P}^{#\bf P}, namely the class of languages that can be decided by a Turing machine in polynomial time given access to an oracle with the power to compute a function in the counting complexity class #{\bf P}. This result which illustrates the power of counting is considered to be a seminal result in computational complexity theory. An analogous result in the complexity theory over the reals (in the sense of Blum-Shub-Smale real Turing machines) has been missing so far. We formulate and prove a real analogue of Toda's theorem. Unlike Toda's proof in the discrete case, which relied on sophisticated combinatorial arguments, our proof is topological in nature. (Joint work with Thierry Zell.)

- Series
- Geometry Topology Working Seminar
- Time
- Friday, April 10, 2009 - 15:00 for 2 hours
- Location
- Skiles 269
- Speaker
- Thang Le – School of Mathematics, Georgia Tech

These are two hour talks.

We will develop general theory of quantum invariants based on sl_2 (the simplest Lie algebra): The Jones polynomials, the colored Jones polynomials, quantum sl_2 groups, operator invariants of tangles, and relations with the Alexander polynomial and the A-polynomials. Optional: Finite type invariants and the Kontsevich integral.

- Series
- Geometry Topology Seminar
- Time
- Monday, April 13, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Uli Walther – Purdue University

Starting with some classical hypergeometric functions, we explain how to derive their classical univariate differential equations. A severe change of coordinates transforms this ODE into a system of PDE's that has nice geometric aspects. This type of system, called A-hypergeometric, was introduced by Gelfand, Graev, Kapranov and Zelevinsky in about 1985. We explain some basic questions regarding these systems. These are addressed through homology, combinatorics, and toric geometry.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, April 13, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Stacey Levine – Duquesne University

We present new finite difference approximations for solving
variational problems using the TV and Besov smoothness penalty
functionals. The first approach reduces oversmoothing and anisotropy
found in common discrete approximations of the TV functional. The
second approach reduces the staircasing effect that arises from TV
type smoothing. The algorithms converge and can be sped up using a
multiscale algorithm. Numerical examples demonstrate both the
qualitative and quantitative behavior of the solutions.

- Series
- Geometry Topology Seminar
- Time
- Monday, April 13, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Roman Golovko – USC

We will define the sutured version of embedded contact homology for sutured contact 3-manifolds. After that, we will show that the sutured version of embedded contact homology of S^1\times D^2, equipped with 2n sutures of integral or infinite slope on the boundary, coincides with the sutured Floer homology.

- Series
- Analysis Seminar
- Time
- Monday, April 13, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Doron Lubinsky – School of Mathematics, Georgia Tech

It turns out that the sinc kernel is not the only kernel that arises as a universality limit coming from random matrices associated with measures with compact support. Any reproducing kernel for a de Branges space that is equivalent to a Paley-Winer space may arise. We discuss this and some other results involving de Branges spaces, universality, and orthogonal polynomials.

- Series
- CDSNS Colloquium
- Time
- Monday, April 13, 2009 - 16:30 for 2 hours
- Location
- Skiles 255
- Speaker
- Konstantin Mischaikow – Rutgers University

I will discuss new computational tools based on topological methods that extracts coarse, but rigorous, combinatorial descriptions of global dynamics of multiparameter nonlinear systems. These techniques are motivated by the fact that these systems can produce an wide variety of complicated dynamics that vary dramatically as a function of changes in the nonlinearities and the following associated challenges which we claim can, at least in part, be addressed. 1. In many applications there are models for the dynamics, but specific parameters are unknown or not directly computable. To identify the parameters one needs to be able to match dynamics produced by the model against that which is observed experimentally. 2. Experimental measurements are often too crude to identify classical dynamical structures such as fixed points or periodic orbits, let alone more the complicated structures associated with chaotic dynamics. 3. Often the models themselves are based on nonlinearities that a chosen because of heuristic arguments or because they are easy to fit to data, as opposed to being derived from first principles. Thus, one wants to be able to separate the scientific conclusions from the particular nonlinearities of the equations. To make the above mentioned comments concrete I will describe the techniques in the context of a simple model arising in population biology.

- Series
- Other Talks
- Time
- Monday, April 13, 2009 - 16:30 for 2 hours
- Location
- Skiles 269
- Speaker
- Jozsef Solymosi – Math, UBC

An old conjecture of Erdos and Szemeredi states that if A is a finite set of integers then the sum-set or the product-set should be large. The sum-set of A is A + A={a+b | a,b \in A\}, and the product set is defined in a similar way, A*A={ab | a,b \in A}. Erdos and Szemeredi conjectured that the sum-set or the product set is almost quadratic in |A|, i.e. max(|A+A|,|A*A|)> c|A|^{2-\epsilon}. In this talk we review some recent developments and problems related to the conjecture.

- Series
- PDE Seminar
- Time
- Tuesday, April 14, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Joy Ko – Brown University, Providence

I will talk about the highlights of a collaborative and multidisciplinary program investigating qualitative features of steady water waves with vorticity in two dimensions. Computational and analytical results together with data from the oceanographic community have resulted in strong evidence that key qualitative features such as amplitude, depth, streamline shape and pressure profile can be fundamentally affected by the presence of vorticity. Systematic studies of constant vorticity and shear vorticity functions will be presented.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, April 15, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Igor Belykh – University of Georgia

- Series
- Research Horizons Seminar
- Time
- Wednesday, April 15, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Sung Ha Kang – School of Mathematics, Georgia Tech

This talk will focus on mathematical approaches using PDE and variational models for image processing. I will discuss general problems arising from image reconstructions and segmentation, starting from Total Variation minimization (TV) model and Mumford-Shah segmentation model, and present new models from various developments. Two main topics will be on variational approaches to image reconstruction and multi-phase segmentation. Many challenges and various problems will be presented with some numerical results.

- Series
- ACO Student Seminar
- Time
- Wednesday, April 15, 2009 - 13:30 for 1 hour (actually 50 minutes)
- Location
- ISyE Executive Classroom
- Speaker
- Luke Postle – School of Mathematics/ACO, Georgia Tech

Grotzsch's Theorem states that every triangle-free planar graph is
3-colorable.
Thomassen conjectured that every triangle-free planar graph has
exponentially many distinct 3-colorings. He proved that it has at least
2^{n^{1/12}/20000} distinct 3-colorings where n is the number of vertices.
We show that it has at least 2^{\sqrt{n/600}} distinct 3-colorings.
Joint work with Arash Asadi and Robin Thomas.

- Series
- Stochastics Seminar
- Time
- Thursday, April 16, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Vladimir I. Koltchinskii – School of Mathematics, Georgia Tech

In binary classification problems, the goal is to estimate a function g*:S -> {-1,1} minimizing the generalization error (or the risk)
L(g):=P{(x,y):y \neq g(x)},
where P is a probability distribution in S x {-1,1}. The distribution P is unknown and estimators \hat g of g* are based on a finite number of independent random couples (X_j,Y_j) sampled from P. It is of interest to have upper bounds on the excess risk
{\cal E}(\hat g):=L(\hat g) - L(g_{\ast})
of such estimators that hold with a high probability and that take into account reasonable measures of complexity of classification problems (such as, for instance, VC-dimension). We will discuss several approaches (both old and new) to excess risk bounds in classification, including some recent results on excess risk in so called active learning.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, April 16, 2009 - 16:30 for 2 hours
- Location
- Skiles 269
- Speaker
- John McCuan – School of Mathematics, Georgia Tech

Archimedes principle may be used to predict if and how certain solid objects float in a liquid bath. The principle, however, neglects to consider capillary forces which can sometimes play an important role. We describe a recent generalization of the principle and how the standard textbook presentation of Archimedes' work may have played a role in delaying the discovery of such generalizations to this late date.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Friday, April 17, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Gilad Lerman – University of Minnesota

Note special day.

We propose a fast multi-way spectral clustering algorithm for multi-manifold data modeling, i.e., modeling data by mixtures of manifolds (possibly intersecting). We describe the supporting theory as well as the practical choices guided by it. We first develop the case of hybrid linear modeling, i.e., when the underlying manifolds are affine subspaces in a Euclidean space, and then we extend this setting to more general manifolds. We exemplify the practical use of the algorithm by demonstrating its successful application to problems of motion segmentation.

- Series
- Combinatorics Seminar
- Time
- Friday, April 17, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Guantao Chen – Georgia State University

Let G be a graph and K be a field. We associate to G a projective toric variety X_G over K, the cut variety of the graph G. The cut ideal I_G of the graph G is the ideal defining the cut variety. In this talk, we show that, if G is a subgraph of a subdivision of a book or an outerplanar graph, then the minimal generators are quadrics. Furthermore we describe the generators of the cut ideal of a subdivision of a book.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, April 17, 2009 - 15:00 for 2 hours
- Location
- Skiles 269
- Speaker
- Thang Le – School of Mathematics, Georgia Tech

These are two hour lectures.

We will develop general theory of quantum invariants based on sl_2 (the simplest Lie algebra): The Jones polynomials, the colored Jones polynomials, quantum sl_2 groups, operator invariants of tangles, and relations with the Alexander polynomial and the A-polynomials. Optional: Finite type invariants and the Kontsevich integral.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, April 20, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Tiancheng Ouyang – Brigham Young

In this talk, I will show many interesting orbits in 2D and 3D of the N-body problem. Some of them do not have symmetrical property nor with equal masses. Some of them with collision singularity. The methods of our numerical optimization lead to search the initial conditions and properties of preassigned orbits. The variational methods will be used for the prove of the existence.

- Series
- Geometry Topology Seminar
- Time
- Monday, April 20, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Scott Baldridge – LSU

In this talk we will introduce the notion of a cube diagram---a surprisingly subtle, extremely powerful new way to represent a knot or link. One of the motivations for creating cube diagrams was to develop a 3-dimensional "Reidemeister's theorem''. Recall that many knot invariants can be easily be proven by showing that they are invariant under the three Reidemeister moves. On the other hand, simple, easy-to-check 3-dimensional moves (like triangle moves) are generally ineffective for defining and proving knot invariants: such moves are simply too flexible and/or uncontrollable to check whether a quantity is a knot invariant or not. Cube diagrams are our attempt to "split the difference" between the flexibility of ambient isotopy of R^3 and specific, controllable moves in a knot projection. The main goal in defining cube diagrams was to develop a data structure that describes an embedding of a knot in R^3 such that (1) every link is represented by a cube diagram, (2) the data structure is rigid enough to easily define invariants, yet (3) a limited number of 5 moves are all that are necessary to transform one cube diagram of a link into any other cube diagram of the same link. As an example of the usefulness of cube diagrams we present a homology theory constructed from cube diagrams and show that it is equivalent to knot Floer homology, one of the most powerful known knot invariants.

- Series
- Analysis Seminar
- Time
- Monday, April 20, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Svitlana Mayboroda – Purdue University

Note special time

In 1908 Hadamard conjectured that the biharmonic Green function must be positive. Later on, several counterexamples to Hadamard's conjecture have been found and a variety of upper estimates were obtained in sufficiently smooth domains. However, the behavior of the Green function in general domains was not well-understood until recently. In a joint work with V. Maz'ya we derive sharp pointwise estimates for the biharmonic and, more generally, polyharmonic Green function in arbitrary domains. Furthermore, we introduce the higher order capacity and establish an analogue of the Wiener criterion describing the precise correlation between the geometry of the domain and the regularity of the solutions to the polyharmonic equation.

- Series
- CDSNS Colloquium
- Time
- Monday, April 20, 2009 - 16:30 for 2 hours
- Location
- Skiles 255
- Speaker
- Jianshe Yu – Guangzhou University

In the talk I will discuss the periodicity of solutions to the classical forced pendulum equation y" + A sin y = f(t) where A= g/l is the ratio of the gravity constant and the pendulum length, and f(t) is an external periodic force with a minimal period T. The major concern is to characterize conditions on A and f under which the equation admits periodic solutions with a prescribed minimal period pT, where p>1 is an integer. I will show how the new approach, based on the critical point theory and an original decomposition technique, leads to the existence of such solutions without requiring p to be a prime as imposed in most previous approaches. In addition, I will present the first non-existence result of such solutions which indicates that long pendulum has a natural resistance to oscillate periodically.

- Series
- ACO Colloquium
- Time
- Tuesday, April 21, 2009 - 16:30 for 2 hours
- Location
- Skiles 255
- Speaker
- Anna Gilbert – University of Michigan, Ann Arbor

The past 10 years have seen a confluence of research in sparse approximation amongst computer science, mathematics, and electrical engineering. Sparse approximation encompasses a large number of mathematical, algorithmic, and signal processing problems which all attempt to balance the size of a (linear) representation of data and the fidelity of that representation. I will discuss several of the basic algorithmic problems and their solutions, focusing on special classes of matrices. I will conclude with an application in biological testing.

- Series
- Graph Theory Seminar
- Time
- Wednesday, April 22, 2009 - 11:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 269
- Speaker
- Matt Baker – School of Mathematics, Georgia Tech

I will discuss some new results, as well as new interpretations of some old results, concerning reduced divisors (a.k.a. G-parking functions) on graphs, metric graphs, and tropical curves.

- Series
- Research Horizons Seminar
- Time
- Wednesday, April 22, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Evans Harrell – School of Mathematics, Georgia Tech

The eigenvalues of the Laplacian are the squares of the frequencies of
the normal modes of vibration, according to the wave equation. For this
reason, Bers and Kac referred to the problem of determining the shape of
a domain from the eigenvalue spectrum of the Laplacian as the question of
whether one can "hear" the shape. It turns out that in general the answer
is "no." Sometimes, however, one can, for instance in extremal cases
where a domain, or a manifold, is round. There are many "isoperimetric"
theorems that allow us to conclude that a domain, curve, or a manifold,
is round, when enough information about the spectrum of the Laplacian
or a similar operator is known. I'll describe a few of these theorems
and show how to prove them by linking geometry with functional analysis.

- Series
- ACO Student Seminar
- Time
- Wednesday, April 22, 2009 - 13:30 for 2 hours
- Location
- ISyE Executive Classroom
- Speaker
- David Cash – Computer Science, Georgia Tech

We construct efficient and natural encryption schemes that remain
secure (in the standard model) even when used to encrypt messages that
may depend upon their secret keys. Our schemes are based on
well-studied "noisy learning" problems. In particular, we design
1) A symmetric-key cryptosystem based on the "learning parity with
noise" (LPN) problem, and
2) A public-key cryptosystem based on the "learning with errors"
(LWE) problem, a generalization of LPN that is at least as hard as
certain worst-case lattice problems (Regev, STOC 2005; Peikert, STOC
2009).
Remarkably, our constructions are close (but non-trivial) relatives of
prior schemes based on the same assumptions --- which were proved
secure only in the usual key-independent sense --- and are nearly as
efficient. For example, our most efficient public-key scheme encrypts
and decrypts in amortized O-tilde(n) time per message bit, and has
only a constant ciphertext expansion factor. This stands in contrast
to the only other known standard-model schemes with provable security
for key-dependent messages (Boneh et al., CRYPTO 2008), which incur a
significant extra cost over other semantically secure schemes based on
the same assumption. Our constructions and security proofs are simple
and quite natural, and use new techniques that may be of independent
interest.
This is joint work with Chris Peikert and Amit Sahai.

- Series
- Analysis Seminar
- Time
- Wednesday, April 22, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Peter D. Miller – University of Michigan

We will discuss a new method of asymptotic analysis of matrix-valued Riemann-Hilbert problems that involves dispensing with analyticity in favor of measured deviation therefrom. This method allows the large-degree analysis of orthogonal polynomials on the real line with respect to varying nonanalytic weights with external fields having two Lipschitz-continuous derivatives, as long as the corresponding equilibrium measure has typical support properties. Universality of local eigenvalue statistics of unitary-invariant ensembles in random matrix theory follows under the same conditions. This is joint work with Ken McLaughlin.

- Series
- Graph Theory Seminar
- Time
- Thursday, April 23, 2009 - 12:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Jie Ma – School of Mathematics, Georgia Tech

A well know theorem of Kuratowski states that a graph is planar graph iff it contains no TK_5 or TK_{3,3}. In 1970s Seymour conjectured that every 5-connected nonplanar graph contains a TK_5. In the talk we will discuss several special cases of the conjecture, for example the graphs containing K_4^- (K_4 withour an edge). A related independent paths theorem also will be covered.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Thursday, April 23, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Per-Gunnar Martinsson – Dept of Applied Mathematics, University of Colorado

Note special day

Linear boundary value problems occur ubiquitously in many areas of
science and engineering, and the cost of computing approximate
solutions to such equations is often what determines which problems
can, and which cannot, be modelled computationally. Due to advances in
the last few decades (multigrid, FFT, fast multipole methods, etc), we
today have at our disposal numerical methods for most linear boundary
value problems that are "fast" in the sense that their computational
cost grows almost linearly with problem size. Most existing "fast"
schemes are based on iterative techniques in which a sequence of
incrementally more accurate solutions is constructed. In contrast, we
propose the use of recently developed methods that are capable of
directly inverting large systems of linear equations in almost linear
time. Such "fast direct methods" have several advantages over
existing iterative methods:
(1) Dramatic speed-ups in applications involving the repeated solution
of similar problems (e.g. optimal design, molecular dynamics).
(2) The ability to solve inherently ill-conditioned problems (such as
scattering problems) without the use of custom designed preconditioners.
(3) The ability to construct spectral decompositions of differential
and integral operators.
(4) Improved robustness and stability.
In the talk, we will also describe how randomized sampling can be used
to rapidly and accurately construct low rank approximations to matrices.
The cost of constructing a rank k approximation to an m x n matrix A
for which an O(m+n) matrix-vector multiplication scheme is available
is O((m+n)*k). This cost is the same as that of the well-established
Lanczos scheme, but the randomized scheme is significantly more robust.
For a general matrix A, the cost of the randomized scheme is O(m*n*log(k)),
which should be compared to the O(m*n*k) cost of existing deterministic
methods.

- Series
- Stochastics Seminar
- Time
- Thursday, April 23, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Yichuan Zhao – Department of Mathematics, Georgia State University

It is of interest that researchers study competing risks in which subjects may fail from any one of k causes. Comparing any two competing risks with covariate effects is very important in medical studies. In this talk, we develop omnibus tests for comparing cause-specific hazard rates and cumulative incidence functions at specified covariate levels. The omnibus tests are derived under the additive risk model by a weighted difference of estimates of cumulative cause-specific hazard rates. Simultaneous confidence bands for the difference of two conditional cumulative incidence functions are also constructed. A simulation procedure is used to sample from the null distribution of the test process in which the graphical and numerical techniques are used to detect the significant difference in the risks. In addition, we conduct a simulation study, and the simulation result shows that the proposed procedure has a good finite sample performance. A melanoma data set in clinical trial is used for the purpose of illustration.

- Series
- Algebra Seminar
- Time
- Thursday, April 23, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Tom Tucker – Univ. of Rochester

Let S be a group or semigroup acting on a variety V, let x be a point on V, and let W be a subvariety of V. What can be said about the structure of the intersection of the S-orbit of x with W? Does it have the structure of a union of cosets of subgroups of S? The Mordell-Lang theorem of Laurent, Faltings, and Vojta shows that this is the case for certain groups of translations (the Mordell conjecture is a consequence of this). On the other hand, Pell's equation shows that it is not true for additive translations of the Cartesian plane. We will see that this question relates to issues in complex dynamics, simple questions from linear algebra, and techniques from the study of linear recurrence sequences.

- Series
- Combinatorics Seminar
- Time
- Friday, April 24, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Mokshay Madiman – Department of Statistics, Yale University

We develop an information-theoretic foundation for compound Poisson
approximation and limit theorems (analogous to the corresponding
developments for the central limit theorem and for simple Poisson
approximation). First, sufficient conditions are given under which the
compound Poisson distribution has maximal entropy within a natural
class of probability measures on the nonnegative integers. In
particular, it is shown that a maximum entropy property is valid
if the measures under consideration are log-concave, but that it
fails in general. Second, approximation bounds in the (strong)
relative entropy sense are given for distributional approximation
of sums of independent nonnegative integer valued random variables
by compound Poisson distributions. The proof techniques involve the
use of a notion of local information quantities that generalize the
classical Fisher information used for normal approximation, as well
as the use of ingredients from Stein's method for compound Poisson
approximation. This work is joint with Andrew Barbour (Zurich),
Oliver Johnson (Bristol) and Ioannis Kontoyiannis (AUEB).

- Series
- Geometry Topology Working Seminar
- Time
- Friday, April 24, 2009 - 15:00 for 2 hours
- Location
- Skiles 269
- Speaker
- Thang Le – School of Mathematics, Georgia Tech

These are two hour lectures.

We will develop general theory of quantum invariants based on sl_2 (the simplest Lie algebra): The Jones polynomials, the colored Jones polynomials, quantum sl_2 groups, operator invariants of tangles, and relations with the Alexander polynomial and the A-polynomials. Optional: Finite type invariants and the Kontsevich integral.

- Series
- Analysis Seminar
- Time
- Monday, April 27, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Tin Yau Tam – Department of Mathematics, Auburn University

Let A be a Hilbert space operator. If A = UP is the polar decomposition of A,
and 0 < \lambda < 1, the \lambda-Aluthge transform of A is defined to be
the operator \Delta_\lambda = P^\lambda UP^{1-\lambda}. We will discuss the recent progress on
the convergence of the iteration. Infinite and finite dimensional cases will be discussed.

- Series
- Dissertation Defense
- Time
- Tuesday, April 28, 2009 - 14:30 for 3 hours
- Location
- Skiles 269
- Speaker
- Alexander Grigo – School of Mathematics, Georgia Tech

- Series
- ACO Seminar
- Time
- Wednesday, April 29, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Jeong Han Kim – Yonsei University and NIMS, South Korea

We consider the problem of finding an unknown graph by using two types of queries with an additive property. Given a graph, an additive query asks the number of edges in a set of vertices while a cross-additive query asks the number of edges crossing between two disjoint sets of vertices. The queries ask sum of weights for the weighted graphs. These types of queries were partially motivated in DNA shotgun sequencing and linkage discovery problem of artificial intelligence. For a given unknown weighted graph G with n vertices, m edges, and a certain mild condition on weights, we prove that there exists a non-adaptive algorithm to find the edges of G using O\left(\frac{m\log n }{\log m}\right) queries of both types provided that m \geq n^{\epsilon} for any constant \epsilon> 0. For a graph, it is shown that the same bound holds for all range of m. This settles a conjecture of Grebinski for finding an unweighted graph using additive queries. We also consider the problem of finding the Fourier coefficients of a certain class of pseudo-Boolean functions. A similar coin weighing problem is also considered. (This is joint work with S. Choi)

- Series
- Analysis Seminar
- Time
- Wednesday, April 29, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Francisco Marcellan – Universidad Carlos III de Madrid

In this contribution we study the asymptotic behaviour of polynomials orthogonal with respect to a Sobolev-Type inner product

\langle p, q\rangle_S = \int^\infty_0 p(x)q(x)x^\alpha e^{-x} dx + IP(0)^t AQ(0), \alpha > -1,

where p and q are polynomials with real coefficients,

A = \pmatrix{M_0 & \lambda\\ \lambda & M_1},
IP(0) = \pmatrix{p(0)\\ p'(0)}, Q(0) = \pmatrix{q(0)\\ q'(0)},

and A is a positive semidefinite matrix.

First, we analyze some algebraic properties of these polynomials. More precisely, the connection relations between the polynomials orthogonal with respect to the above inner product and the standard Laguerre polynomials are deduced. On the other hand, the symmetry of the multiplication operator by x^2 yields a five term recurrence relation that such polynomials satisfy.

Second, we focus the attention on their outer relative asymptotics with respect to the standard Laguerre polynomials as well as on an analog of the Mehler-Heine formula for the rescaled polynomials.

Third, we find the raising and lowering operators associated with these orthogonal polynomials. As a consequence, we deduce the holonomic equation that they satisfy. Finally, some open problems will be considered.

- Series
- PDE Seminar
- Time
- Tuesday, May 5, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Giuseppe Savare – Università degli Studi di Pavia, Italy

Some interesting nonlinear fourth-order parabolic equations, including the "thin-film" equation with linear mobility and the quantum drift-diffusion equation, can be seen as gradient flows of first-order integral functionals in the Wasserstein space of probability measures. We will present some general tools of the metric-variational approach to gradient flows which are useful to study this kind of equations and their asymptotic behavior. (Joint works in collaboration with U.Gianazza, R.J. McCann, D. Matthes, G. Toscani)

- Series
- Dissertation Defense
- Time
- Monday, May 11, 2009 - 13:00 for 2 hours
- Location
- Skiles 255
- Speaker
- Evan Borenstein – School of Mathematics, Georgia Tech

- Series
- Combinatorics Seminar
- Time
- Thursday, May 21, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Joshua Cooper – Department of Mathematics, University of South Carolina

We consider the Ulam "liar" and "pathological liar" games, natural and well-studied variants of "20 questions" in which the adversarial respondent is permitted to lie some fraction of the time. We give an improved upper bound for the optimal strategy (aka minimum-size covering code), coming within a triply iterated log factor of the so-called "sphere covering" lower bound. The approach is twofold: (1) use a greedy-type strategy until the game is nearly over, then (2) switch to applying the "liar machine" to the remaining Berlekamp position vector. The liar machine is a deterministic (countable) automaton which we show to be very close in behavior to a simple random walk, and this resemblance translates into a nearly optimal strategy for the pathological liar game.

- Series
- Graph Theory Seminar
- Time
- Thursday, June 4, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Zdenek Dvorak – Simon Fraser University

Richter and Salazar conjectured that graphs that are critical for a fixed crossing number k have bounded bandwidth. A weaker well-known conjecture of Richter is that their maximum degree is bounded in terms of k. We disprove these conjectures for every k >170, by providing examples of k-crossing-critical graphs with arbitrarily large maximum degree, and explore the structure of such graphs.

- Series
- Graph Theory Seminar
- Time
- Thursday, June 11, 2009 - 11:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Daniel Kral – ITI, Charles University, Prague

We study several parameters of cubic graphs with large girth. In particular, we prove that every n-vertex cubic graph with sufficiently large girth satisfies the following:

- has a dominating set of size at most 0.29987n (which improves the previous bound of 0.32122n of Rautenbach and Reed)
- has fractional chromatic number at most 2.37547 (which improves the previous bound of 2.66881 of Hatami and Zhu)
- has independent set of size at least 0.42097n (which improves the previous bound of 0.41391n of Shearer), and
- has fractional total chromatic number arbitrarily close to 4 (which answers in the affirmative a conjecture of Reed). More strongly, there exists g such that the fractional total chromatic number of every bridgeless graph with girth at least g is equal to 4.

The presentation is based on results obtained jointly with Tomas Kaiser, Andrew King, Petr Skoda and Jan Volec.

- Series
- Other Talks
- Time
- Wednesday, July 1, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Pablo Laguna – School of Physics, Georgia Tech

This will be an informal seminar with a discussion on some mathematical problems in relativistic astrophysics, and discuss plans for future joint seminars between the Schools of Mathematics and Physics.

- Series
- Dissertation Defense
- Time
- Wednesday, July 1, 2009 - 15:30 for 3 hours
- Location
- Skiles 255
- Speaker
- Alan J. Michaels – School of Electrical and Computer Engineering, Georgia Tech

This disseratation provides the conceptual development, modeling and simulation, physical implementation and measured hardware results for a procticable digital coherent chaotic communication system.

- Series
- Dissertation Defense
- Time
- Thursday, July 2, 2009 - 13:30 for 2.5 hours
- Location
- Skiles 255
- Speaker
- Turkay Yolcu – School of Mathematics, Georgia Tech

In this thesis, we extend De Giorgi's interpolation method to a class of parabolic equations which are not gradient flows but possess an entropy functional and an underlying Lagrangian. The new fact in the study is that not only the
Lagrangian may depend on spatial variables, but also it does not induce a metric. Assuming the initial condition is a density function, not necessarily smooth, but solely of bounded first moments and finite entropy, we use a variational scheme to
discretize the equation in time and construct approximate solutions. Moreover, De
Giorgi's interpolation method reveals to be a powerful tool for proving convergence
of our algorithm. Finally, we analyze uniqueness and stability of our solution in L^1.

- Series
- Dissertation Defense
- Time
- Monday, August 10, 2009 - 15:00 for 2 hours
- Location
- Skiles 255
- Speaker
- Kun Zhao – School of Mathematics, Georgia Tech

- Series
- Dissertation Defense
- Time
- Friday, August 14, 2009 - 14:00 for 2 hours
- Location
- Skiles 114
- Speaker
- Hao Deng – School of Mathematics, Georgia Tech

- Series
- Combinatorics Seminar
- Time
- Friday, August 14, 2009 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Prof. Satoru Iwata – Kyoto University

In this lecture, I will explain connections between graph theory and submodular optimization. The topics include theorems of Nash-Williams on orientation and detachment of graphs.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Tuesday, August 18, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Justin W. L. Wan – Computer Science, University of Waterloo

In image guided procedures such as radiation therapies and computer-assisted surgeries, physicians often need to align images that are taken at different times and by different modalities. Typically, a rigid registration is performed first, followed by a nonrigid registration. We are interested in efficient registrations methods which are robust (numerical solution procedure will not get stuck at local minima) and fast (ideally real time). We will present a robust continuous mutual information model for multimodality regisration and explore the new emerging parallel hardware for fast computation. Nonrigid registration is then applied afterwards to further enhance the results. Elastic and fluid models were usually used but edges and small details often appear smeared in the transformed templates. We will propose a new inviscid model formulated in a particle framework, and derive the corresponding nonlinear partial differential equations for computing the spatial transformation. The idea is to simulate the template image as a set of free particles moving toward the target positions under applied forces. Our model can accommodate both small and large deformations, with sharper edges and clear texture achieved at less computational cost. We demonstrate the performance of our model on a variety of images including 2D and 3D, mono-modal and multi-modal, synthetic and clinical data.

- Series
- Combinatorics Seminar
- Time
- Wednesday, August 19, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Satoru Iwata – Kyoto University

In this lecture, I will review combinatorial algorithms for minimizing submodular functions. In particular, I will present a new combinatorial algorithm obtained in my recent joint work with Jim Orlin.

- Series
- Combinatorics Seminar
- Time
- Friday, August 21, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Satoru Iwata – Kyoto University

In this lecture, I will explain the greedy approximation algorithm on submodular function maximization due to Nemhauser, Wolsey, and Fisher. Then I will apply this algorithm to the problem of approximating an monotone submodular functions by another submodular function with succinct representation. This approximation method is based on the maximum volume ellipsoid inscribed in a centrally symmetric convex body. This is joint work with Michel Goemans, Nick Harvey, and Vahab Mirrokni.

- Series
- CDSNS Colloquium
- Time
- Monday, August 24, 2009 - 16:30 for 2 hours
- Location
- Skiles 255
- Speaker
- Qian Wang – School of Mathematics, Georgia Tech

The Bendixson conditions for general nonlinear differential equations in Banach spaces are developed in terms of stability of associated compound differential equations. The generalized Bendixson criterion states that, if some measure of 2-dimensional surface area tends to zero with time, then there are no closed curves that are left invariant by the dynamics. In particular, there are no nontrivial periodic orbits, homoclinic loops or heteroclinic loops. Concrete conditions that preclude the existence of periodic solutions for a parabolic PDE will be given. This is joint work with Professor James S. Muldowney at University of Alberta.

- Series
- PDE Seminar
- Time
- Tuesday, August 25, 2009 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- David Hoff – Indiana University, Bloomington

We prove that solutions of the Navier-Stokes equations of
three-dimensional, compressible flow, restricted to fluid-particle
trajectories, can be extended as analytic functions of complex time. One
important corollary is backwards uniqueness: if two such solutions agree
at a given time, then they must agree at all previous times.
Additionally, analyticity yields sharp estimates for the time
derivatives of arbitrary order of solutions along particle trajectories.
I'm going to integrate into the talk something like a "pretalk" in an
attempt to motivate the more technical material and to make things
accessible to a general analysis audience.

- Series
- ACO Student Seminar
- Time
- Wednesday, August 26, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- SyE Executive Classroom
- Speaker
- Ton Dieker – School of Industrial and Systems Engineering, Georgia Tech

A central question in the theory of card shuffling is how quickly a deck of
cards becomes 'well-shuffled' given a shuffling rule. In this talk, I will
discuss a probabilistic card shuffling model known as the 'interchange
process'. A
conjecture from 1992 about this model has recently been resolved
and I will address how my work has been involved with this conjecture. I
will also discuss other card shuffling models.

- Series
- Analysis Seminar
- Time
- Wednesday, August 26, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Michael Lacey – Georgia Institute of Technology

We will survey recent developments in the area of two weight inequalities, especially those relevant for singular integrals. In the second lecture, we will go into some details of recent characterizations of maximal singular integrals of the speaker, Eric Sawyer, and Ignacio Uriate-Tuero.

- Series
- School of Mathematics Colloquium
- Time
- Wednesday, August 26, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Chemistry and Biochemistry Boggs Building, Room B-6A
- Speaker
- Abhay Ashtekar – Department of Physics and Institute for Gravitational Physics and Geometry, Pennsylvania State University – ashtekar@gravity.psu.edu

Pre-reception at 2:30 in Room N201. If you would like to meet with Prof. Ashtekar while he is on campus (at the Center for Relativistic Astrophysics - Boggs building), please contact <A class="moz-txt-link-abbreviated" href="mailto:lori.federico@physics.gatech.edu">lori.federico@physics.gatech.edu</a>.

General relativity is based on a deep interplay between physics and mathematics: Gravity is encoded in geometry. It has had spectacular observational success and has also pushed forward the frontier of geometric analysis. But the theory is incomplete because it ignores quantum physics. It predicts that the space-time ends at singularities such as the big-bang. Physics then comes to a halt. Recent developments in loop quantum gravity show that these predictions arise because the theory has been pushed beyond the domain of its validity. With new inputs from mathematics, one can extend cosmology beyond the big-bang. The talk will provide an overview of this new and rich interplay between physics and mathematics.

- Series
- Graph Theory Seminar
- Time
- Thursday, August 27, 2009 - 12:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- William T. Trotter – Math, GT

Slightly modifying a quote of
Paul Erdos: The problem for graphs we
solve this week. The corresponding problem
for posets will take longer.
As one example, testing a graph to determine
if it is planar is linear in the number of
edges. Testing an order (Hasse) diagram to
determine if it is planar is NP-complete.
As a second example, it is NP-complete
to determine whether a graph is a cover
graph.
With these remarks in mind, we present
some results, mostly new but some classic,
regarding posets with planar cover graphs
and planar diagrams. The most recent
result is that for every h, there is a constant
c_h so that if P is a poset of height h and
the cover graph of P is planar, then
the dimension of P is at most c_h.

- Series
- Stochastics Seminar
- Time
- Thursday, August 27, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Dabao Zhang – Purdue University

We propose a penalized orthogonal-components regression
(POCRE) for large p small n data. Orthogonal components are sequentially
constructed to maximize, upon standardization, their correlation to the
response residuals. A new penalization framework, implemented via
empirical Bayes thresholding, is presented to effectively identify
sparse predictors of each component. POCRE is computationally efficient
owing to its sequential construction of leading sparse principal
components. In addition, such construction offers other properties such
as grouping highly correlated predictors and allowing for collinear or
nearly collinear predictors. With multivariate responses, POCRE can
construct common components and thus build up latent-variable models for
large p small n data. This is an joint work with Yanzhu Lin and Min Zhang

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, August 31, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Nicola Guglielmi – Università di L&#039;Aquila – guglielm@univaq.it

In this talk I will address the problem of the computation of the jointspectral radius (j.s.r.) of a set of matrices.This tool is useful to determine uniform stability properties of non-autonomous discrete linear systems. After explaining how to extend the spectral radius from a single matrixto a set of matrices and illustrate some applications where such conceptplays an important role I will consider the problem of the computation ofthe j.s.r. and illustrate some possible strategies. A basic tool I willuse to this purpose consists of polytope norms, both real and complex.I will illustrate a possible algorithm for the computation of the j.s.r. ofa family of matrices which is based on the use of these classes of norms.Some examples will be shown to illustrate the behaviour of the algorithm.Finally I will address the problem of the finite computability of the j.s.r.and state some recent results, open problems and conjectures connected withthis issue.

- Series
- Geometry Topology Seminar
- Time
- Monday, August 31, 2009 - 14:01 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 269
- Speaker
- Rinat Kashaev – Section de Mathématiques Université de Genève – Rinat.Kashaev@unige.ch

Not yet!

- Series
- PDE Seminar
- Time
- Tuesday, September 1, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Lincoln Chayes – UCLA

This seminar concerns the analysis of a PDE, invented by J.M. Lasry
and P.L. Lions
whose applications need not concern us.
Notwithstanding, the focus of the application is the behavior of a
free boundary in a diffusion equation which has dynamically evolving,
non--standard sources. Global existence and uniqueness are
established for this system. The work to be discussed represents a
collaborative effort with
Maria del Mar Gonzalez, Maria Pia Gualdani and Inwon Kim.

- Series
- Other Talks
- Time
- Wednesday, September 2, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- John Etnyre – Ga Tech

In these talks we will introduced the basic definitions and examples of presheaves, sheaves and sheaf spaces. We will also explore various constructions and properties of these objects.

- Series
- Analysis Seminar
- Time
- Wednesday, September 2, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Michael Lacey – Georgia Institute of Technology

We will survey recent developments in the area of two weight inequalities, especially those relevant for singular integrals. In the second lecture, we will go into some details of recent characterizations of maximal singular integrals of the speaker, Eric Sawyer, and Ignacio Uriate-Tuero.

- Series
- ACO Student Seminar
- Time
- Wednesday, September 2, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- ISyE Executive Classroom
- Speaker
- Ernie Croot – School of Mathematics

Sum-Product inequalities originated in the early 80's
with the work of Erdos and Szemeredi, who showed that there exists
a constant c such that if A is a set of n integers, n sufficiently
large, then either the sumset A+A = {a+b : a,b in A} or the product
set A.A = {ab : a,b in A}, must exceed n^(1+c) in size. Since that
time the subject has exploded with a vast number of generalizations
and extensions of the basic result, which has led to many
very interesting unsolved problems (that would make great thesis
topics). In this talk I will survey some of the developments in this
fast-growing area.

- Series
- Graph Theory Seminar
- Time
- Thursday, September 3, 2009 - 12:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- William T. Trotter – School of Mathematics, Georgia Tech

We will discuss the classic theorem of Walter Schnyder: a graph G is planar if and only if the dimension of its incidence poset is at most 3. This result has been extended by Brightwell and Trotter to show that the dimension of the vertex-edge-face poset of a planar 3-connected graph is 4 and the removal of any vertex (or by duality, any face) reduces the dimension to 3. Recently, this result and its extension to planar multigraphs was key to resolving the question of the dimension of the adjacency poset of a planar bipartite graph. It also serves to motivate questions about the dimension of posets with planar cover graphs.

- Series
- Stochastics Seminar
- Time
- Thursday, September 3, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Philippe Rigollet – Princeton University

The goal of this talk is to present a new method for sparse estimation
which does not use standard techniques such as $\ell_1$ penalization.
First, we introduce a new setup for aggregation which bears strong links
with generalized linear models and thus encompasses various response
models such as Gaussian regression and binary classification. Second, by
combining maximum likelihood estimators using exponential weights we
derive a new procedure for sparse estimations which satisfies exact
oracle inequalities with the desired remainder term. Even though the
procedure is simple, its implementation is not straightforward but it
can be approximated using the Metropolis algorithm which results in a
stochastic greedy algorithm and performs surprisingly well in a
simulated problem of sparse recovery.

- Series
- Math Physics Seminar
- Time
- Thursday, September 3, 2009 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Lincoln Chayes – UCLA – lchayes@math.ucla.edu

The McK--V system is a non--linear diffusion equation with a non--local
non--linearity provided by convolution. Recently popular in a variety
of applications, it enjoys an ancient heritage as a basis for
understanding equilibrium and near equilibrium fluids. The model is
discussed in finite volume where, on the basis of the physical
considerations, the correct scaling (for the model itself) is
identified. For dimension two and above and in large volume, the phase
structure of the model is completely elucidated in (somewhat
disturbing) contrast to dynamical results. This seminar represents
joint work with V. Panferov.

- Series
- SIAM Student Seminar
- Time
- Friday, September 4, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Maria Reguera Rodriguez – Georgia Tech – mreguera@math.gatech.edu

In this talk we will review some of the classical weighted theory for singular integral operators, and discuss some recent progress on finding sharp bounds in terms of the A_p constant associated with the weight

- Series
- Combinatorics Seminar
- Time
- Friday, September 4, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Karthekeyan Chandrasekaran – College of Computing

Lovasz Local Lemma (LLL) is a powerful result in probability theory that states that the probability that none of a set of bad events happens is nonzero if the probability of each event is small compared to the number of events that depend on it. It is often used in combination with the probabilistic method for non-constructive existence proofs. A prominent application of LLL is to k-CNF formulas, where LLL implies that, if every clause in the formula shares variables with at most d \le 2^k/e other clauses then such a formula has a satisfying assignment. Recently, a randomized algorithm to efficiently construct a satisfying assignment was given by Moser. Subsequently Moser and Tardos gave a randomized algorithm to construct the structures guaranteed by the LLL in a very general algorithmic framework. We will address the main problem left open by Moser and Tardos of derandomizing their algorithm efficiently when the number of other events that any bad event depends on is possibly unbounded. An interesting special case of the open problem is the k-CNF problem when k = \omega(1), that is, when k is more than a constant.

- Series
- Geometry Topology Seminar
- Time
- Monday, September 7, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- -
- Speaker
- - – -

- Series
- PDE Seminar
- Time
- Tuesday, September 8, 2009 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Konstantina Trivisa – University of Maryland, College Park

Multicomponent reactive flows arise in many practical applicationssuch as combustion, atmospheric modelling, astrophysics, chemicalreactions, mathematical biology etc. The objective of this work isto develop a rigorous mathematical theory based on the principles ofcontinuum mechanics. Results on existence, stability, asymptotics as wellas singular limits will be discussed.

- Series
- Research Horizons Seminar
- Time
- Wednesday, September 9, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 171
- Speaker
- Ernie Croot – School of Mathematics, Georgia Tech – ecroot@math.gatech.edu

Additive combinatorics is a relatively new field, with
many diverse and exciting research programmes. In this talk I will discuss
two of these programmes -- the continuing development of
sum-product inequalities, and the unfolding progress on
arithmetic progressions -- along with some new results proved by me and my
collaborators. Hopefully I will have time to mention some nice research
problems as well.

- Series
- ACO Student Seminar
- Time
- Wednesday, September 9, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- ISyE Executive Classroom
- Speaker
- Steve Tyber – ISyE, Georgia Tech

In 1969, Gomory introduced the master group polyhedron for pure integer programs and derives the mixed integer cut (MIC) as a facet of a special family of these polyhedra. We study the MIC in this framework, characterizing both its facets and extreme points; next, we extend our results under mappings between group polyhedra; and finally, we conclude with related open problems. No prior knowledge of algebra or the group relaxation is assumed. Terminology will be introduced as needed. Joint work with Ellis Johnson.

- Series
- Other Talks
- Time
- Wednesday, September 9, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- John Etnyre – Ga Tech

In these talks we will introduced the basic definitions and examples of presheaves, sheaves and sheaf spaces. We will also explore various constructions and properties of these objects.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Wednesday, September 9, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 114
- Speaker
- Amy Novick-Cohen – Technion

Grain boundaries within polycrystalline materials are known to be governed by motion by mean curvature. However, when the polycrystalline specimen is thin, such as in thin films, then the effects of the exterior surfaces start to play an important role. We consider two particularly simple geometries, an axi-symmetric geometry, and a half loop geometry which is often employed in making measurements of the kinetic coefficient in the motion by mean curvature equation, obtaining corrective terms which arise due to the coupling of grain boundaries to the exterior surface. Joint work with Anna Rotman, Arkady Vilenkin & Olga Zelekman-Smirin

- Series
- Analysis Seminar
- Time
- Wednesday, September 9, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Shannon Bishop – Georgia Tech

We describe how time-frequency analysis is used to analyze boundedness
and Schatten class properties of pseudodifferential operators and
Fourier integral operators.

- Series
- Stochastics Seminar
- Time
- Thursday, September 10, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Christian Houdré – Georgia Tech

Given a random word of size n whose letters are drawn independently<br />

from an ordered alphabet of size m, the fluctuations of the shape of<br />

the corresponding random RSK Young tableaux are investigated, when both<br />

n and m converge together to infinity. If m does not grow too fast and<br />

if the draws are uniform, the limiting shape is the same as the<br />

limiting spectrum of the GUE. In the non-uniform case, a control of<br />

both highest probabilities will ensure the convergence of the first row<br />

of the tableau, i.e., of the length of the longest increasing<br />

subsequence of the random word, towards the Tracy-Widom distribution.

- Series
- SIAM Student Seminar
- Time
- Friday, September 11, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Ruoting Gong – Georgia Tech – rgong@math.gatech.edu

We develop a stochastic control system from a continuous-time
Principal-Agent model in which both the principal and the agent have
imperfect information and different beliefs about the project. We
attempt to optimize the agent’s utility function under the agent’s
belief. Via the corresponding Hamilton-Jacobi-Bellman equation we
prove that the value function is jointly continuous and satisfies the
Dynamic Programming Principle. These properties directly lead to the
conclusion that the value function is a viscosity solution of the HJB
equation. Uniqueness is then also established.

- Series
- Probability Working Seminar
- Time
- Friday, September 11, 2009 - 15:00 for 2 hours
- Location
- Skiles 154
- Speaker
- Sergio Almada – Georgia Tech

The talk is based on the recent paper by M.Hairer, J.Mattingly, and M.Scheutzow with the same title.There are many Markov chains on infinite dimensional spaces whose one-step
transition kernels are mutually singular when starting from different initial
conditions. We give results which prove unique ergodicity under minimal
assumptions on one hand and the existence of a spectral gap under conditions
reminiscent of Harris' theorem. The first uses the existence of couplings which
draw the solutions together as time goes to infinity. Such "asymptotic
couplings" were central to recent work on SPDEs on which this work builds. The
emphasis here is on stochastic differential delay equations.Harris' celebrated
theorem states that if a Markov chain admits a Lyapunov function whose level
sets are "small" (in the sense that transition probabilities are uniformly
bounded from below), then it admits a unique invariant measure and transition
probabilities converge towards it at exponential speed. This convergence takes
place in a total variation norm, weighted by the Lyapunov function. A second
aim of this article is to replace the notion of a "small set" by the much
weaker notion of a "d-small set," which takes the topology of the underlying
space into account via a distance-like function d. With this notion at hand, we
prove an analogue to Harris' theorem, where the convergence takes place in a
Wasserstein-like distance weighted again by the Lyapunov function. This
abstract result is then applied to the framework of stochastic delay equations.

- Series
- Combinatorics Seminar
- Time
- Friday, September 11, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Jinwoo Shin – MIT

We consider the #P complete problem of counting the number of independent
sets in a given graph. Our interest is in understanding the effectiveness of
the popular Belief Propagation (BP) heuristic. BP is a simple and iterative
algorithm that is known to have at least one fixed point. Each fixed point
corresponds to a stationary point of the Bethe free energy (introduced by
Yedidia, Freeman and Weiss (2004) in recognition of Hans Bethe's earlier
work (1935)). The evaluation of the Bethe Free Energy at such a stationary
point (or BP fixed point) leads to the Bethe approximation to the number of
independent sets of the given graph. In general BP is not known to converge
nor is an efficient, convergent procedure for finding stationary points of
the Bethe free energy known. Further, effectiveness of Bethe approximation
is not well understood.
As the first result of this paper, we propose a BP-like algorithm that
always converges to a BP fixed point for any graph. Further, it finds an \epsilon
approximate fixed point in poly(n, 2^d, 1/\epsilon) iterations for a graph of n
nodes with max-degree d. As the next step, we study the quality of this
approximation. Using the recently developed 'loop series' approach by
Chertkov and Chernyak, we establish that for any graph of n nodes with
max-degree d and girth larger than 8d log n, the multiplicative error decays
as 1 + O(n^-\gamma) for some \gamma > 0. This provides a deterministic counting
algorithm that leads to strictly different results compared to a recent
result of Weitz (2006). Finally as a consequence of our results, we prove
that the Bethe approximation is exceedingly good for a random 3-regular
graph conditioned on the Shortest Cycle Cover Conjecture of Alon and Tarsi
(1985) being true.
(Joint work with Venkat Chandrasekaran, Michael Chertkov, David Gamarnik and
Devavrat Shah)

- Series
- Geometry Topology Working Seminar
- Time
- Friday, September 11, 2009 - 15:00 for 2 hours
- Location
- Skiles 269
- Speaker
- John Etnyre – Georgia Tech

We will discuss how to put a hyperbolic structure on various
surface and 3-manifolds. We will being by discussing isometries of hyperbolic space in
dimension 2 and 3. Using our understanding of these isometries we will explicitly
construct hyperbolic structures on all close surfaces of genus greater than one and a
complete finite volume hyperbolic structure on the punctured torus. We will then consider
the three dimensional case where we will concentrate on putting hyperbolic structures on
knot complements. (Note: this is a 2 hr seminar)

- Series
- CDSNS Colloquium
- Time
- Monday, September 14, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Jose M. Arrieta – Universidad Complutense de Madrid

We study the behavior of the asymptotic dynamics of a dissipative reaction-diffusion equation in a dumbbell domain, which, roughly speaking, consists of two fixed domains joined by a thin channel. We analyze the behavior of the stationary solutions (solutions of the elliptic problem), their local unstable manifold and the attractor of the equation as the width of the connecting channel goes to zero.

- Series
- Geometry Topology Seminar
- Time
- Monday, September 14, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Dishant M. Pancholi – International Centre for Theoretical Physics, Trieste, Italy

After reviewing a few techniques from the theory of confoliation in dimension three we will discuss some generalizations and certain obstructions in extending these techniques to higher dimensions. We also will try to discuss a few questions regarding higher dimensional confoliations.

- Series
- Other Talks
- Time
- Monday, September 14, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Student Services Building, Auditorium 117
- Speaker
- Richard Tapia – Rice University

In this talk Professor Tapia identifies elementary mathematical frameworks for the study of popular drag racing beliefs. In this manner some myths are validated while others are destroyed. Tapia will explain why dragster acceleration is greater than the acceleration due to gravity, an age old inconsistency. His "Fundamental Theorem of Drag Racing" will be presented. The first part of the talk will be a historical account of the development of drag racing and will include several lively videos.

- Series
- Geometry Topology Seminar
- Time
- Monday, September 14, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Christian Zickert – UC Berkeley – zickert@math.berkeley.edu

A closed hyperbolic 3-manifold $M$ determines a fundamental classin the algebraic K-group $K_3^{ind}(C)$. There is a regulator map$K_3^{ind}(C)\to C/4\Pi^2Z$, which evaluated on the fundamental classrecovers the volume and Chern-Simons invariant of $M$. The definition of theK-groups are very abstract, and one is interested in more concrete models.The extended Bloch is such a model. It is isomorphic to $K_3^{ind}(C)$ andhas several interesting properties: Elements are easy to produce; thefundamental class of a hyperbolic manifold can be constructed explicitly;the regulator is given explicitly in terms of a polylogarithm.

- Series
- PDE Seminar
- Time
- Tuesday, September 15, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Zhang, Lei – University of Florida – leizhang@math.ufl.edu

Many problems in Geometry, Physics and Biology are described by nonlinear partial differential equations of second order or four order. In this talk I shall mainly address the blow-up phenomenon in a class of fourth order equations from conformal geometry and some Liouville systems from Physics and Ecology. There are some challenging open problems related to these equations and I will report the recent progress on these problems in my joint works with Gilbert Weinstein and Chang-shou Lin.

- Series
- ACO Student Seminar
- Time
- Wednesday, September 16, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- ISyE Executive Classroom
- Speaker
- Shabbir Ahmed – Georgia Tech, ISyE

I will describe a simple scheme for generating a valid inequality for a
stochastic integer programs from a given valid inequality for its
deterministic counterpart. Applications to stochastic lot-sizing problems
will be discussed. This is joint work with Yongpei Guan and George Nemhauser
and is based on the following two papers
(1) Y. Guan, S. Ahmed and G.L. Nemhauser. "Cutting planes for multi-stage
stochastic integer programs," Operations Research, vol.57, pp.287-298, 2009
(2)
Y. Guan, S. Ahmed and G. L. Nemhauser. "Sequential pairing of mixed integer
inequalities," Discrete Optimization, vol.4, pp.21-39, 2007
This is a joint DOS/ACO seminar.

- Series
- Research Horizons Seminar
- Time
- Wednesday, September 16, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 171
- Speaker
- William T. Trotter – School of Mathematics, Georgia Tech – trotter@math.gatech.edu

(joint work with Csaba Biro, Dave Howard, Mitch Keller and Stephen Young. Biro and Young finished their Ph.D.'s at Georgia Tech in 2008. Howard and Keller will graduate in spring 2010)

Motivated by questions in algebra involving what is called "Stanley" depth, the following combinatorial question was posed to us by Herzog: Given a positive integer n, can you partition the family of all non-empty subsets of {1, 2, ..., n} into intervals, all of the form [A, B] where |B| is at least n/2. We answered this question in the affirmative by first embedding it in a stronger result and then finding two elegant proofs. In this talk, which will be entirely self-contained, I will give both proofs. The paper resulting from this research will appear in the Journal of Combinatorial Theory, Series A.

- Series
- Other Talks
- Time
- Wednesday, September 16, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- John Etnyre – Ga Tech

In these talks we will introduced the basic definitions and examples of presheaves, sheaves and sheaf spaces. We will also explore various constructions and properties of these objects.

- Series
- Graph Theory Seminar
- Time
- Thursday, September 17, 2009 - 12:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- William T. Trotter – Math, GT

This is the third session in this series and a special effort will be made to make it self contained ... to the fullest extent possible.With Felsner and Li, we proved that the dimension of the adjacency poset of a graph is bounded as a function of the genus. For planar graphs, we have an upper bound of 8 and for outerplanar graphs, an upper bound of 5. For lower bounds, we have respectively 5 and 4. However, for bipartite planar graphs, we have an upper bound of 4, which is best possible. The proof of this last result uses the Brightwell/Trotter work on the dimension of thevertex/edge/face poset of a planar graph, and led to the following conjecture:For each h, there exists a constant c_h so that if P is a poset of height h and the cover graph of P is planar, then the dimension of P is at most c_h.With Stefan Felsner, we have recently resolved this conjecture in the affirmative. From below, we know from a construction of Kelly that c_h must grow linearly with h.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, September 18, 2009 - 14:00 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 269
- Speaker
- John Etnyre – Georgia Tech

We will discuss how to put a hyperbolic structure on various surface and 3-manifolds. We will being by discussing isometries of hyperbolic space in dimension 2 and 3. Using our understanding of these isometries we will explicitly construct hyperbolic structures on all close surfaces of genus greater than one and a complete finite volume hyperbolic structure on the punctured torus. We will then consider the three dimensional case where we will concentrate on putting hyperbolic structures on knot complements. (Note: this is a 1.5 hr lecture)

- Series
- CDSNS Colloquium
- Time
- Monday, September 21, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Federico Bonetto – School of Mathematics, Georgia Tech

Fourier's Law assert that the heat flow through a point in a solid is proportional to the temperature gradient at that point. Fourier himself thought that this law could not be derived from the mechanical properties of the elementary constituents (atoms and electrons, in modern language) of the solid. On the contrary, we now believe that such a derivation is possible and necessary. At the core of this change of opinion is the introduction of probability in the description. We now see the microscopic state of a system as a probability measure on phase space so that evolution becomes a stochastic process. Macroscopic properties are then obtained through averages. I will introduce some of the models used in this research and discuss their relevance for the physical problem and the mathematical results one can obtain.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, September 21, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Yuliya Babenko – Department of Mathematics and Statistics, Sam Houston State University

In this talk we first present the exact asymptotics of the optimal
error in the weighted L_p-norm, 1\leq p \leq \infty, of linear spline
interpolation of an arbitrary bivariate function f \in C^2([0,1]^2). We
further discuss the applications to numerical integration and adaptive
mesh generation for finite element methods, and explore connections
with the problem of approximating the convex bodies by polytopes. In
addition, we provide the generalization to asymmetric norms.
We give a brief review of known results and introduce a series of new
ones. The proofs of these results lead to algorithms for the
construction of asymptotically optimal sequences of triangulations for
linear interpolation.
Moreover, we derive similar results for other classes of splines and
interpolation schemes, in particular for splines over rectangular
partitions.
Last but not least, we also discuss several multivariate
generalizations.

- Series
- Geometry Topology Seminar
- Time
- Monday, September 21, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Doug LaFountain – SUNY - Buffalo

The uniform thickness property (UTP) is a property of knots embeddedin the 3-sphere with the standard contact structure. The UTP was introduced byEtnyre and Honda, and has been useful in studying the Legendrian and transversalclassification of cabled knot types. We show that every iterated torus knotwhich contains at least one negative iteration in its cabling sequence satisfiesthe UTP. We also conjecture a complete UTP classification for iterated torusknots, and fibered knots in general.

- Series
- Other Talks
- Time
- Tuesday, September 22, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- ISyE Executive Classroom, Main Building
- Speaker
- Michael J. Todd – School of Operations Research and Information Engineering, Cornell University

We discuss the convergence properties of first-order methods for two problems that
arise in computational geometry and statistics: the minimum-volume enclosing ellipsoid problem
and the minimum-area enclosing ellipsoidal cylinder problem for a set of m points in R^n.
The algorithms are old but the analysis is new, and the methods are remarkably effective
at solving large-scale problems to high accuracy.

- Series
- Mathematical Finance/Financial Engineering Seminar
- Time
- Tuesday, September 22, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Gunter Meyer – School of Mathematics, Georgia Tech

When the asset price follows geometric Brownian motion but allows random Poisson jumps (called jump diffusion) then the standard Black Scholes partial differential for the option price becomes a partial-integro differential equation (PIDE). If, in addition, the volatility of the diffusion is assumed to lie between given upper and lower bounds but otherwise not known then sharp upper and lower bounds on the option price can be found from the Black Scholes Barenblatt equation associated with the jump diffusion PIDE. In this talk I will introduce the model equations and then discuss the computational issues which arise when the Black Scholes Barenblatt PIDE for jump diffusion is to be solved numerically.

- Series
- PDE Seminar
- Time
- Tuesday, September 22, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Shigeaki Koike – Saitama University, Japan

We discuss comparison principle for viscosity solutions of fully nonlinear elliptic PDEs in $\R^n$ which may have superlinear growth in $Du$ with variable coefficients. As an example, we keep the following PDE in mind:$$-\tr (A(x)D^2u)+\langle B(x)Du,Du\rangle +\l u=f(x)\quad \mbox{in }\R^n,$$where $A:\R^n\to S^n$ is nonnegative, $B:\R^n\to S^n$ positive, and $\l >0$. Here $S^n$ is the set of $n\ti n$ symmetric matrices. The comparison principle for viscosity solutions has been one of main issues in viscosity solution theory. However, we notice that we do not know if the comparison principle holds unless $B$ is a constant matrix. Moreover, it is not clear which kind of assumptions for viscosity solutions at $\infty$ is suitable. There seem two choices: (1) one sided boundedness ($i.e.$ bounded from below), (2) growth condition.In this talk, assuming (2), we obtain the comparison principle for viscosity solutions. This is a work in progress jointly with O. Ley.

- Series
- Research Horizons Seminar
- Time
- Wednesday, September 23, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 171
- Speaker
- Stavros Garoufalidis – Georgia Tech School of Mathematics – stavros@math.gatech.edu

Dodgson (the author of Alice in Wonderland) was an amateur
mathematician who wrote a book about determinants in 1866 and gave a copy
to the queen. The queen dismissed the book and so did the math community
for over a century. The Hodgson Condensation method resurfaced in the 80's
as the fastest method to compute determinants (almost always, and almost
surely). Interested about Lie groups, and their representations? In
crystal bases? In cluster algebras? In alternating sign matrices?
OK, how about square ice? Are you nuts? If so, come and listen.

- Series
- Other Talks
- Time
- Wednesday, September 23, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Matt Baker – School of Mathematics, Georgia Tech

I will discuss how various geometric categories (e.g. smooth manifolds, complex manifolds) can be be described in terms of locally ringed spaces. (A locally ringed space is a topological spaces endowed with a sheaf of rings whose stalks are local rings.) As an application of the notion of locally ringed space, I'll define what a scheme is.

- Series
- Analysis Seminar
- Time
- Wednesday, September 23, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Maxym Yattselev – Vanderbilt University

We consider multipoint Padé approximation to Cauchy transforms of
complex measures. First, we recap that if the support of a measure is
an analytic Jordan arc and if the measure itself is absolutely
continuous with respect to the equilibrium distribution of that arc
with Dini-continuous non-vanishing density, then the diagonal
multipoint Padé approximants associated with appropriate interpolation
schemes converge locally uniformly to the approximated Cauchy
transform in the complement of the arc. Second, we show that this
convergence holds also for measures whose Radon–Nikodym derivative is
a Jacobi weight modified by a Hölder continuous function. The
asymptotics behavior of Padé approximants is deduced from the analysis
of underlying non–Hermitian orthogonal polynomials, for which the
Riemann–Hilbert–∂ method is used.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, September 24, 2009 - 11:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Distinguished Professor Craig Tracy – University of California, Davis

The asymmetric simple exclusion process (ASEP) is a continuous time Markov process of interacting particles on a lattice \Gamma. ASEP is defined by two rules: (1) A particle at x \in \Gamma waits an exponential time with parameter one, and then chooses y \in \Gamma with probability p(x, y); (2) If y is vacant at that time it moves to y, while if y is occupied it remains at x. The main interest lies in infinite particle systems. In this lecture we consider the ASEP on the integer lattice {\mathbb Z} with nearest neighbor jump rule: p(x, x+1) = p, p(x, x-1) = 1-p and p \ne 1/2. The integrable structure is that of Bethe Ansatz. We discuss various limit theorems which in certain cases establishes KPZ universality.

- Series
- Stochastics Seminar
- Time
- Thursday, September 24, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Jim Nolen – Duke University

I will describe recent work on the behavior of solutions to
reaction diffusion equations (PDEs) when the coefficients in the
equation are random. The solutions behave like traveling waves moving
in a randomly varying environment. I will explain how one can obtain
limit theorems (Law of Large Numbers and CLT) for the motion of the
interface. The talk will be accessible to people without much knowledge
of PDE.

- Series
- SIAM Student Seminar
- Time
- Friday, September 25, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Benjamin Webb – School of Mathematics, Georgia Tech

In the study of one dimensional dynamical systems one often assumes that the functions involved have a negative Schwarzian derivative. In this talk we consider a generalization of this condition. Specifically, we consider the interval functions of a real variable having some iterate with a negative Schwarzian derivative and show that many known results generalize to this larger class of functions. The introduction of this class was motivated by some maps arising in neuroscience

- Series
- Geometry Topology Working Seminar
- Time
- Friday, September 25, 2009 - 15:00 for 2 hours
- Location
- Skiles 269
- Speaker
- Anh Tran – Georgia Tech

(This is a 2 hour lecture.)

In this talk I will give a quick review of classical invariants of
Legendrian knots in a 3-dimensional contact manifold (the topological knot type, the
Thurston-Bennequin invariant and the rotation number). These classical invariants do not
completely determine the Legendrian isotopy type of Legendrian knots, therefore we will
consider Contact homology (aka Chekanov-Eliashberg DGA), a new invariant that has been
defined in recent years. We also discuss the linearization of Contact homology, a method
to extract a more computable invariant out of the DGA associated to a Legendrian knot.

- Series
- Combinatorics Seminar
- Time
- Friday, September 25, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Mihyun Kang – Technische Universitat Berlin

Since the seminal work of Erdos and Renyi the phase transition of the largest components in random graphs became one of the central topics in random graph theory and discrete probability theory. Of particular interest in recent years are random graphs with constraints (e.g. degree distribution, forbidden substructures) including random planar graphs. Let G(n,M) be a uniform random graph, a graph picked uniformly at random among all graphs on vertex set [n]={1,...,n} with M edges. Let P(n,M) be a uniform random planar graph, a graph picked uniformly at random among all graphs on vertex set [n] with M edges that are embeddable in the plane. Erodos-Renyi, Bollobas, and Janson-Knuth-Luczak-Pittel amongst others studied the critical behaviour of the largest components in G(n,M) when M= n/2+o(n) with scaling window of size n^{2/3}. For example, when M=n/2+s with s=o(n) and s \gg n^{2/3}, a.a.s. (i.e. with probability tending to 1 as n approaches \infty) G(n,M) contains a unique largest component (the giant component) of size (4+o(1))s. In contract to G(n,M) one can observe two critical behaviour in P(n,M), when M=n/2+o(n) with scaling window of size n^{2/3}, and when M=n+o(n) with scaling window of size n^{3/5}. For example, when M=n/2+s with s = o(n) and s \gg n^{2/3}, a.a.s. the largest component in P(n,M) is of size (2+o(1))s, roughly half the size of the largest component in G(n,M), whereas when M=n+t with t = o(n) and t \gg n^{3/5}, a.a.s. the number of vertices outside the giant component is \Theta(n^{3/2}t^{-3/2}). (Joint work with Tomasz Luczak)

- Series
- Probability Working Seminar
- Time
- Friday, September 25, 2009 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 154
- Speaker
- Linwei Xin – Georgia Tech

In this talk, we will introduce the classical Cramer's Theorem. The
pattern of proof is one of the two most powerful tools in the theory
of large deviations. Namely, the upper bound comes from optimizing
over a family of Chebychef inequalities; while the lower bound comes
from introducing a Radon-Dikodym factor in order to make what was
originally "deviant" behavior look like typical behavior.
If time permits, we will extend the Cramer's Theorem to a more general
setting and discuss the Sanov Theorem.
This talk is based on Deuschel and Stroock's .

- Series
- CDSNS Colloquium
- Time
- Monday, September 28, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Federico Bonetto – School of Mathematics, Georgia Tech

This talk continues from last week's colloquium.

Fourier's Law assert that the heat flow through a point in a solid is proportional to the temperature gradient at that point. Fourier himself thought that this law could not be derived from the mechanical properties of the elementary constituents (atoms and electrons, in modern language) of the solid. On the contrary, we now believe that such a derivation is possible and necessary. At the core of this change of opinion is the introduction of probability in the description. We now see the microscopic state of a system as a probability measure on phase space so that evolution becomes a stochastic process. Macroscopic properties are then obtained through averages. I will introduce some of the models used in this research and discuss their relevance for the physical problem and the mathematical results one can obtain.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, September 28, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Chad Topaz – Macalester College

Biological aggregations such as insect swarms, bird flocks, and fish schools are arguably some of the most common and least understood patterns in nature. In this talk, I will discuss recent work on swarming models, focusing on the connection between inter-organism social interactions and properties of macroscopic swarm patterns. The first model is a conservation-type partial integrodifferential equation (PIDE). Social interactions of incompressible form lead to vortex-like swarms. The second model is a high-dimensional ODE description of locust groups. The statistical-mechanical properties of the attractive-repulsive social interaction potential control whether or not individuals form a rolling migratory swarm pattern similar to those observed in nature. For the third model, we again return to a conservation-type PIDE and, via long- and short-wave analysis, determine general conditions that social interactions must satisfy for the population to asymptotically spread, contract, or reach steady state.

- Series
- Geometry Topology Seminar
- Time
- Monday, September 28, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Vera Vertesi – MSRI

Legendrian knots are knots that can be described only by their projections(without having to separately keep track of the over-under crossinginformation): The third coordinate is given as the slope of theprojections. Every knot can be put in Legendrian position in many ways. Inthis talk we present an ongoing project (with Etnyre and Ng) of thecomplete classification of Legendrian representations of twist knots.

- Series
- PDE Seminar
- Time
- Tuesday, September 29, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Stephen Pankavich – University of Texas, Arlington

We formulate a plasma model in which negative ions tend to a fixed, spatially-homogeneous background of positive charge. Instead of solutions with compact spatial support, we must consider those that tend to the background as x tends to infinity. As opposed to the traditional Vlasov-Poisson system, the total charge and energy are thus infinite, and energy conservation (which is an essential component of global existence for the traditional problem) cannot provide bounds for a priori estimates. Instead, a conserved quantity related to the energy is used to bound particle velocities and prove the existence of a unique, global-in-time, classical solution. The proof combines these energy estimates with a crucial argument which establishes spatial decay of the charge density and electric field.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, September 30, 2009 - 11:00 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 269
- Speaker
- Jan Medlock – Clemson University – medlock@clemson.edu

The recent emergence of the influenza strain (the "swine flu") and delays in production of vaccine against it illustrate the importance of optimizing vaccine allocation. Using an age-dependent model parametrized with data from the 1957 and 1918 influenza pandemics, which had dramatically different mortality patterns, we determined optimal vaccination strategies with regard to five outcome measures: deaths, infections, years of life lost, contingent valuation and economic costs. In general, there is a balance between vaccinating children who transmit most and older individuals at greatest risk of mortality, however, we found that when at least a moderate amount of an effective vaccine is available supply, all outcome measures prioritized vaccinating schoolchildren. This is vaccinating those most responsible for transmission to indirectly protect those most at risk of mortality and other disease complications. When vaccine availability or effectiveness is reduced, the balance is shifted toward prioritizing those at greatest risk for some outcome measures. The amount of vaccine needed for vaccinating schoolchildren to be optimal depends on the general transmissibility of the influenza strain (R_0). We also compared the previous and new recommendations of the CDC and its Advisory Committee on Immunization Practices are below optimum for all outcome measures. In addition, I will discuss some recent results using mortality and hospitalization data from the novel H1N1 "swine flu" and implications of the delay in vaccine availability.

- Series
- Research Horizons Seminar
- Time
- Wednesday, September 30, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 171
- Speaker
- Brett Wick – School of Mathematics, Georgia Tech – wick@math.gatech.edu

In the last 10 years there has been a resurgence of interest in questions about certain spaces of analytic functions. In this talk we will discuss various advances in the study of these spaces of functions and highlight questions of current interest in analytic function theory. We will give an overview of recent advances in the Corona Problem, bilinear forms on spaces of analytic functions, and highlight some methods to studying these questions that use more discrete techniques.

- Series
- Other Talks
- Time
- Wednesday, September 30, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Matt Baker – School of Mathematics, Georgia Tech

After a few remarks to tie up some loose ends from last week's talk on locally
ringed spaces, I will discuss exact sequences of sheaves and give some natural
examples coming from real, complex, and algebraic geometry. In the context of these
examples, we'll see that a surjective map of sheaves (meaning a morphism of sheaves
which is surjective on the level of stalks) need not be surjective on global
sections. This observation will be used to motivate the need for "sheaf cohomology"
(which will be discussed in detail in subsequent talks).

- Series
- Analysis Seminar
- Time
- Wednesday, September 30, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Plamen Illiev – Georgia Tech

The trigonometric Grassmannian parametrizes specific solutions of the KP hierarchy which correspond to rank one solutions of a differential-difference bispectral problem. It can be considered as a completion of the phase spaces of the trigonometric Calogero-Moser particle system or the rational Ruijsenaars-Schneider system.
I will describe the characterization of this Grassmannian in terms of representation theory of a suitable difference W-algebra. Based on joint work with L. Haine and E. Horozov.

- Series
- Dissertation Defense
- Time
- Thursday, October 1, 2009 - 14:00 for 2 hours
- Location
- Skiles 255
- Speaker
- Mitch Keller – School of Mathematics, Georgia Tech

Tanenbaum, Trenk, and Fishburn introduced the concept of linear discrepancy in 2001, proposing it as a way to measure a partially ordered set's distance from being a linear order. In addition to proving a number of results about linear discrepancy, they posed eight challenges and questions for future work. This dissertation completely resolves one of those challenges and makes contributions on two others. This dissertation has three principal components: 3-discrepancy irreducible posets of width 3, degree bounds, and online algorithms for linear discrepancy. The first principal component of this dissertation provides a forbidden subposet characterization of the posets with linear discrepancy equal to 2 by completing the determination of the posets that are 3-irreducible with respect to linear discrepancy. The second principal component concerns degree bounds for linear discrepancy and weak discrepancy, a parameter similar to linear discrepancy. Specifically, if every point of a poset is incomparable to at most \Delta other points of the poset, we prove three bounds: the linear discrepancy of an interval order is at most \Delta, with equality if and only if it contains an antichain of size \Delta+1; the linear discrepancy of a disconnected poset is at most \lfloor(3\Delta-1)/2\rfloor; and the weak discrepancy of a poset is at most \Delta-1. The third principal component of this dissertation incorporates another large area of research, that of online algorithms. We show that no online algorithm for linear discrepancy can be better than 3-competitive, even for the class of interval orders. We also give a 2-competitive online algorithm for linear discrepancy on semiorders and show that this algorithm is optimal.

- Series
- Stochastics Seminar
- Time
- Thursday, October 1, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Denis Bell – University of North Florida

The Black‐Scholes model for stock price as geometric Brownian motion, and the
corresponding European option pricing formula, are standard tools in mathematical
finance. In the late seventies, Cox and Ross developed a model for stock price based
on a stochastic differential equation with fractional diffusion coefficient. Unlike the
Black‐Scholes model, the model of Cox and Ross is not solvable in closed form, hence
there is no analogue of the Black‐Scholes formula in this context. In this talk, we
discuss a new method, based on Stratonovich integration, which yields explicitly
solvable arbitrage‐free models analogous to that of Cox and Ross. This method gives
rise to a generalized version of the Black‐Scholes partial differential equation. We
study solutions of this equation and a related ordinary differential equation.

- Series
- SIAM Student Seminar
- Time
- Friday, October 2, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Shannon Bishop – Georgia Tech – sbishop@math.gatech.edu

I will describe some interesting properties of frames and Gabor frames in particular. Then we will examine how frames may lead to interesting decompositions of integral operators. In particular, I will share some theorems for pseudodifferential operators and Fourier integral operators arising from Gabor frames.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, October 2, 2009 - 15:00 for 2 hours
- Location
- Skiles 269
- Speaker
- Igor Belegradek – Georgia Tech

This 2 hour talk is a gentle introduction to simply-connected sugery theory (following classical work by Browder, Novikov, and Wall). The emphasis will be on classification of high-dimensional manifolds and understanding concrete examples.

- Series
- Probability Working Seminar
- Time
- Friday, October 2, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 154
- Speaker
- Stas Minsker – School of Mathematics, Georgia Tech

The talk is based on the paper by B. Klartag. It will be shown that there exists a sequence \eps_n\to 0 for which the
following holds: let K be a compact convex subset in R^n with nonempty
interior and X a random vector uniformly distributed in K. Then there
exists a unit vector v, a real number \theta and \sigma^2>0 such that
d_TV(, Z)\leq \eps_n
where Z has Normal(\theta,\sigma^2) distribution and d_TV - the total
variation distance. Under some additional assumptions on X, the
statement is true for most vectors v \in R^n.

- Series
- Combinatorics Seminar
- Time
- Friday, October 2, 2009 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Farbod Shokrieh – Georgia Tech – farbod@gatech.edu

It is known that, relative to any fixed vertex q of a finite graph, there
exists a unique q-reduced divisor (G-Parking function based at q) in
each linear equivalence class of divisors.
In this talk, I will give an efficient algorithm for finding such reduced
divisors. Using this, I will give an explicit and efficient bijection
between the Jacobian group and the set of spanning trees of the graph. Then
I will outline some applications of the main results, including a new
approach to the Random Spanning Tree problem, efficient computation of the
group law in the critical and sandpile group, efficient algorithm for the
chip-firing game of Baker and Norine, and the relation to the Riemann-Roch
theory on finite graphs.

- Series
- Geometry Topology Seminar
- Time
- Monday, October 5, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- -
- Speaker
- - – -

- Series
- Research Horizons Seminar
- Time
- Wednesday, October 7, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 171
- Speaker
- Stavros Garoufalidis – School of Mathematics, Georgia Tech – stavros@math.gatech.edu

In linear algebra classes we learn that a symmetic matrix with
real entries has real eigenvalues. But many times we deal with nonsymmetric
matrices that we want them to have real eigenvalues and be stable under a
small perturbation. In the 1930's totally positive matrices were discovered
in mechanical problems of vibtrations, then lost for over 50 years. They
were rediscovered in the 1990's as esoteric objects in quantum groups and
crystal bases. In the 2000's these matrices appeared in relation to
Teichmuller space and its quantization. I plan to give a high school
introduction to totally positive matrices.

- Series
- Other Talks
- Time
- Wednesday, October 7, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Matt Baker – School of Mathematics, Georgia Tech

We will define the Cech cohomology groups of a sheaf and discuss some basic properties of the Cech construction.

- Series
- Analysis Seminar
- Time
- Wednesday, October 7, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Ramazan Tinaztepe – Georgia Tech

Modulation spaces are a class of Banach spaces which provide a quantitative time-frequency analysis of functions via the Short-Time Fourier Transform. The modulation spaces are the "right" spaces for time-frequency analysis andthey occur in many problems in the same way that Besov Spaces are attached to wavelet theory and issues of smoothness. In this seminar, I will talk about embeddings of modulation Spaces into BMO or VMO (the space of functions of bounded or vanishing mean oscillation, respectively ). Membership in VMO is central to the Balian-Low Theorem, which is a cornerstone of time-frequency analysis.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, October 8, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Laura DeMarco – Department of Mathematics, Statistics, and Computer Science, University of Illinois, Chicago

A classification of the dynamics of polynomials in one complex variable has remained elusive, even when considering only the simpler "structurally stable" polynomials. In this talk, I will describe the basics of polynomial iteration, leading up to recent results in the direction of a complete classification. In particular, I will describe a (singular) metric on the complex plane induced by the iteration of a polynomial. I will explain how this geometric structure relates to topological conjugacy classes within the moduli space of polynomials.

- Series
- Graph Theory Seminar
- Time
- Thursday, October 8, 2009 - 12:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Ye Luo – Electrical and Computer Engineering, Georgia Tech

A metric graph is a geometric realization of a finite graph by identifying each edge with a real interval. A divisor on a metric graph Gamma is an element of the free abelian group on Gamma. The rank of a divisor on a metric graph is a concept appearing in the Riemann-Roch theorem for metric graphs (or tropical curves) due to Gathmann and Kerber, and Mikhalkin and Zharkov. A rank-determining set of a metric graph Gamma is defined to be a subset A of Gamma such that the rank of a divisor D on Gamma is always equal to the rank of D restricted on A. I will present an algorithm to derive the reduced divisor from any effective divisor in the same linear system, and show constructively that there exist finite rank-determining sets. Based on this discovery, we can compute the rank of an arbitrary divisor on any metric graph. In addition, I will discuss the properties of rank-determining sets in general and formulate a criterion for rank-determining sets.

- Series
- SIAM Student Seminar
- Time
- Friday, October 9, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Allen Hoffmeyer – School of Mathematics, Georgia Tech

This talk is based on a paper by Medvedev and Scaillet which derives closed form
asymptotic expansions for option implied volatilities (and option prices).
The model is a two-factor jump-diffusion stochastic volatility one with short time to
maturity. The authors derive a power series expansion (in log-moneyness and time
to maturity) for the implied volatility of near-the-money options with small time to
maturity. In this talk, I will discuss their techniques and results.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, October 9, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Igor Belegradek – Georgia Tech

This 2 hour talk is a gentle introduction to simply-connected sugery
theory (following classical work by Browder, Novikov, and Wall). The
emphasis will be on classification of high-dimensional manifolds and
understanding concrete examples.

- Series
- Stochastics Seminar
- Time
- Friday, October 9, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 154 (Unusual time and room)
- Speaker
- Carl Mueller – University of Rochester

One of the most important stochastic partial differential equations,
known as the superprocess, arises as a limit in population dynamics.
There are several notions of uniqueness, but for many years only weak
uniqueness was known. For a certain range of parameters, Mytnik and
Perkins recently proved strong uniqueness. I will describe joint work
with Barlow, Mytnik and Perkins which proves nonuniqueness for the
parameters not included in Mytnik and Perkins' result. This
completely settles the question for strong uniqueness, but I will end
by giving some problems which are still open.

- Series
- Combinatorics Seminar
- Time
- Friday, October 9, 2009 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Ernie Croot – School of Math, Georgia Tech

In this talk I will discuss a new technique discovered by myself
and Olof Sisask which produces many new insights in additive combinatorics,
not to mention new
proofs of classical theorems previously proved only using harmonic
analysis. Among these new proofs is one for Roth's theorem on three-term
arithmetic progressions, which gives the best bounds so
far achieved by any combinatorial method. And another is a new proof
that positive density subsets of the integers mod p contain very
long arithmetic progressions, first proved by Bourgain, and improved
upon by Ben Green and Tom Sanders. If time permits, I will discuss
how the method can be applied to the 2D corners problem.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, October 12, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Wei Zhu – University of Alabama (Department of Mathematics) – wzhu7@bama.ua.edu

The Rudin-Osher-Fatemi (ROF) model is one of the most powerful and popular models in image denoising. Despite its simple form, the ROF functional has proved to be nontrivial to minimize by conventional methods. The difficulty is mainly due to the nonlinearity and poor conditioning of the related problem. In this talk, I will focus on the minimization of the ROF functional in the one-dimensional case. I will present a new algorithm that arrives at the minimizer of the ROF functional fast and exactly. The proposed algorithm will be compared with the standard and popular gradient projection method in accuracy, efficiency and other aspects.

- Series
- Geometry Topology Seminar
- Time
- Monday, October 12, 2009 - 14:05 for 2 hours
- Location
- Skiles 269
- Speaker
- Henry Segerman – UTexas Austin – henrys@math.utexas.edu

The deformation variety is similar to the representation variety inthat it describes (generally incomplete) hyperbolic structures on3-manifolds with torus boundary components. However, the deformationvariety depends crucially on a triangulation of the manifold: theremay be entire components of the representation variety which can beobtained from the deformation variety with one triangulation but notanother, and it is unclear how to choose a "good" triangulation thatavoids these problems. I will describe the "extended deformationvariety", which deals with many situations that the deformationvariety cannot. In particular, given a manifold which admits someideal triangulation we can construct a triangulation such that we canrecover any irreducible representation (with some trivial exceptions)from the associated extended deformation variety.

- Series
- Mathematical Finance/Financial Engineering Seminar
- Time
- Tuesday, October 13, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Suzanne Lee – College of Management, Georgia Tech

We propose a new two stage semi-parametric test and estimation procedure to
investigate predictability of stochastic jump arrivals in asset prices. It allows us
to search for conditional information that affects the likelihood of jump occurrences up
to the intra-day levels so that usual factor analysis for jump dynamics can be
achieved. Based on the new theory of inference, we find empirical evidence of jump clustering
in U.S. individual equity markets during normal trading hours. We also present other
intra-day jump predictors such as analysts recommendation updates and stock news
releases.

- Series
- PDE Seminar
- Time
- Tuesday, October 13, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Xiaoming Wang – Florida State University

We study the asymptotic behavior of the infinite Darcy-Prandtl number Darcy-Brinkman-Boussinesq model for convection in porous media at small Brinkman-Darcy number. This is a singular limit involving a boundary layer with thickness proportional to the square root of the Brinkman-Darcynumber . This is a joint work with Jim Kelliher and Roger Temam.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, October 14, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Bart Haegeman – INRIA, Montpellier, France

Hubbell's neutral model provides a rich theoretical framework to study
ecological communities. By coupling ecological and evolutionary time
scales, it allows investigating how communities are shaped by speciation
processes. The speciation model in the basic neutral model is particularly
simple, describing speciation as a point mutation event in a birth of a
single individual. The stationary species abundance distribution of the
basic model, which can be solved exactly, fits empirical data of
distributions of species abundances surprisingly well. More realistic
speciation models have been proposed such as the random fission model in
which new species appear by splitting up existing species. However, no
analytical solution is available for these models, impeding quantitative
comparison with data. Here we present a self-consistent approximation
method for the neutral community model with random fission speciation. We
derive explicit formulas for the stationary species abundance
distribution, which agree very well with simulations. However, fitting the
model to tropical tree data sets, we find that it performs worse than the
original neutral model with point mutation speciation.

- Series
- Research Horizons Seminar
- Time
- Wednesday, October 14, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 171
- Speaker
- Sung Ha Kang – School of Mathematics, Georgia Tech – kang@math.gatech.edu

Image segmentation has been widely studied, specially since Mumford-Shah
functional was been proposed. Many theoretical works as well as numerous
extensions have been studied rough out the years. This talk will focus on
introduction to these image segmentation functionals. I will start with
the review of Mumford-Shah functional and discuss Chan-Vese model. Some
new extensions will be presented at the end.

- Series
- Other Talks
- Time
- Wednesday, October 14, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- John Etnyre – Ga Tech

We will briefly review the definition of the Cech cohomology groups of a sheaf (so if you missed last weeks talk, you should still be able to follow this weeks), discuss some basic properties of the Cech construction and give some computations that shows how the theory connects to other things (like ordinary cohomology and line bundles).

- Series
- Applied and Computational Mathematics Seminar
- Time
- Wednesday, October 14, 2009 - 13:00 for 8 hours (full day)
- Location
- Skiles 269
- Speaker
- Edson Denis Leonel – Universidade Estadual Paulista, Rio Claro, Brazil

Fermi acceleration is a phenomenon where a classical particle canacquires unlimited energy upon collisions with a heavy moving wall. Inthis talk, I will make a short review for the one-dimensional Fermiaccelerator models and discuss some scaling properties for them. Inparticular, when inelastic collisions of the particle with the boundaryare taken into account, suppression of Fermi acceleration is observed.I will give an example of a two dimensional time-dependent billiardwhere such a suppression also happens.

- Series
- Analysis Seminar
- Time
- Wednesday, October 14, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Marcus Carlsson – Purdue University

Given an "infinite symmetric matrix" W we give a simple condition, related
to the shift operator being expansive on a certain sequence space, under
which W is positive. We apply this result to AAK-type theorems for
generalized Hankel operators, providing new insights related to previous
work by S. Treil and A. Volberg. We also discuss applications and open
problems.

- Series
- Analysis Seminar
- Time
- Thursday, October 15, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255 **NOTE ROOM CHANGE AND SPECIAL DAY**
- Speaker
- Lillian Wong – University of Oklahoma

In this talk, I will discuss some results obtained in my Ph.D. thesis.
First, the point mass formula will be introduced. Using the formula, we
shall see how the asymptotics of orthogonal polynomials relate to the
perturbed Verblunsky coefficients. Then I will discuss two classes of
measures on the unit circle -- one with Verblunsky coefficients \alpha_n -->
0 and the other one with \alpha_n --> L (non-zero) -- and explain the
methods I used to tackle the point mass problem involving these measures.
Finally, I will discuss the point mass problem on the real line. For a long
time it was believed that point mass perturbation will generate
exponentially small perturbation on the recursion coefficients. I will
demonstrate that indeed there is a large class of measures such that that
proposition is false.

- Series
- SIAM Student Seminar
- Time
- Friday, October 16, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Tianjun Ye – Georgia Tech

This talk considers the following sequence shufling problem: Given a biological sequence (either DNA or protein) s, generate a random instance among all the permutations of s that exhibit the same frequencies of k-lets (e.g. dinucleotides, doublets of amino acids, triplets, etc.). Since certain biases in the usage of k-lets are fundamental to biological sequences, effective generation of such sequences is essential for the evaluation of the results of many sequence analysis tools. This talk introduces two sequence shuffling algorithms: A simple swapping-based algorithm is shown to generate a near-random instance and appears to work well, although its efficiency is unproven; a generation algorithm based on Euler tours is proven to produce a precisely uniforminstance, and hence solve the sequence shuffling problem, in time not much more than linear in the sequence length.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, October 16, 2009 - 15:00 for 2 hours
- Location
- Skiles 169
- Speaker
- Amey Kaloti – Georgia Tech

This is a 2-hour talk.

Heegaard floer homology is an invariant of closed 3 manifolds defined by Peter
Ozsvath and Zoltan Szabo. It has proven to be a very strong invariant of 3 manifolds with
connections to contact topology. In these talks we will try to define the Heegaard Floer
homology without assuming much background in low dimensional topology. One more goal is
to present the combinatorial description for this theory.

- Series
- Combinatorics Seminar
- Time
- Friday, October 16, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Nina Balcan – Computing Science &amp; Systems, Georgia Tech

There has been substantial work on approximation algorithms for clustering
data under distance-based objective functions such as k-median, k-means, and
min-sum objectives. This work is fueled in part by the hope that
approximating these objectives well will indeed yield more accurate
solutions. That is, for problems such as clustering proteins by function, or
clustering images by subject, there is some unknown correct "target"
clustering and the implicit assumption is that clusterings that are
approximately optimal in terms of these distance-based measures are also
approximately correct in terms of error with respect to the target. In this
work we show that if we make this implicit assumption explicit -- that is, if
we assume that any c-approximation to the given clustering objective Phi is
epsilon-close to the target -- then we can produce clusterings that are
O(epsilon)-close to the target, even for values c for which obtaining a
c-approximation is NP-hard. In particular, for the k-median, k-means, and
min-sum objectives, we show that we can achieve this guarantee for any
constant c > 1.
Our results show how by explicitly considering the alignment between the
objective function used and the true underlying clustering goals, one can
bypass computational barriers and perform as if these objectives were
computationally substantially easier.
This talk is based on joint work with Avrim Blum and Anupam Gupta (SODA
2009), Mark Braverman (COLT 2009), and Heiko Roeglin and Shang-Hua Teng (ALT 2009).

- Series
- CDSNS Colloquium
- Time
- Monday, October 19, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Redouane Qesmi – York University, Canada and SoM, Georgia Tech

Despite advances in treatment of chronic hepatitis B virus (HBV) infection,
liver transplantation remains the only hope for many patients with end-stage
liver disease due to HBV. A complication with liver transplantation,
however, is that the new liver is eventually reinfected in chronic HBV
patients by infection in other compartments of the body. We have formulated
a model to describe the dynamics of HBV after liver transplant, considering
the liver and the blood of areas of infection. Analyzing the model, we
observe that the system shows either a transcritical or a backward
bifurcation. Explicit conditions on the model parameters are given for the
backward bifurcation to be present, to be reduced, or disappear.
Consequently, we investigate possible factors that are responsible for
HBV/HCV infection and assess control strategies to reduce HBV/HCV
reinfection and improve graft survival after liver transplantation.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, October 19, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Helga S. Huntley – University of Delaware

Biologists tracking crab larvae, engineers designing pollution mitigation strategies, and
climate scientists studying tracer transport in the oceans are among many who rely on
trajectory predictions from ocean models. State-of-the-art models have been shown to
produce reliable velocity forecasts for 48-72 hours, yet the predictability horizon for
trajectories and related Lagrangian quantities remains significantly shorter. We
investigate the potential for decreasing Lagrangian prediction errors by applying a
constrained normal mode analysis (NMA) to blend drifter observations with model velocity
fields. The properties of an unconstrained NMA and the effects of parameter choices are
discussed. The constrained NMA technique is initially presented in a perfect model
simulation, where the “true” velocity field is known and the resulting error can be
directly assessed. Finally, we will show results from a recent experiment in the East
Asia Sea, where real observations were assimilated into operational ocean model hindcasts.

- Series
- Geometry Topology Seminar
- Time
- Monday, October 19, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Inanc Baykur – Brandeis University

We will introduce new constructions of infinite families of smooth structures on small 4-manifolds and infinite families of smooth knottings of surfaces.

- Series
- Analysis Working Seminar
- Time
- Monday, October 19, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Brett Wick – Georgia Tech

In this working seminar we will give a proof of Seip's characterization of interpolating sequences in the Bergman space of analytic functions. This topic has connection with complex analysis, harmonic analysis, and
time frequency analysis and so hopefully many of the participants would
be able to get something out of the seminar. The initial plan will be
to work through his 1993 Inventiones Paper and supplement this with
material from his book "Interpolation and Sampling in Spaces of
Analytic Functions". Notes will be generated as the seminar progresses.

- Series
- Graph Theory Seminar
- Time
- Tuesday, October 20, 2009 - 12:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Gelasio Salazar – Universidad Autonoma de San Luis Potosi

In 1865, Sylvester posed the following problem: For a region R in the plane,let q(R) denote the probability that four points chosen at random from Rform a convex quadrilateral. What is the infimum q* of q(R) taken over allregions R? The number q* is known as Sylvester's Four Point Problem Constant(Sylvester's Constant for short). At first sight, it is hard to imagine howto find reasonable estimates for q*. Fortunately, Scheinerman and Wilf foundthat Sylvester's Constant is intimately related to another fundamentalconstant in discrete geometry. The rectilinear crossing number of rcr(K_n)the complete graph K_n is the minimum number of crossings of edges in adrawing of K_n in the plane in which every edge is a straight segment. Itis not difficult to show that the limit as n goes to infinity ofrcr(K_n)/{n\choose 4} exists; this is the rectilinear crossing numberconstant RCR. Scheinerman and Wilf proved a surprising connection betweenthese constants: q* = RCR. Finding estimates of rcr(K_n) seems like a moreapproachable task. A major breakthrough was achieved in 2003 by Lovasz,Vesztergombi, Wagner, and Welzl, and simultaneously by Abrego andFernandez-Merchant, who unveiled an intimate connection of rcr(K_n) withanother classical problem of discrete geometry, namely the number of

- Series
- Mathematical Finance/Financial Engineering Seminar
- Time
- Tuesday, October 20, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Daniel Bauer – Georgia State University

In recent literature, different mothods have been proposed on how to define
and model stochastic mortality. In most of these approaches, the so-called spot force
of mortality is modeled as a stochastic process. In contrast to such spot force
models, forward force mortality models infer dynamics on the entire
age/term-structure of mortality.
This paper considers forward models defined based on best-estimate forecasts of
survival probabilities as can be found in so-called best-estimate generation life
tables. We provide a detailed analysis of forward mortality models deriven by
finite-dimensional Brownian motion. In particular, we address the relationship to
other modeling approaches, the consistency problem of parametric forward models, and
the existence of finite dimensional realizations for Gaussian forward models. All
results are illustrated based on a simple example with an affine specification.

- Series
- PDE Seminar
- Time
- Tuesday, October 20, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Hongqiu Chen – University of Memphis

Under the classical small-amplitude, long wave-length assumptions in which the
Stokes number is of order one, so featuring a balance between nonlinear and dispersive effects,
the KdV-equation
u_t+ u_x + uu_x + u_xxx = 0 (1)
and the regularized long wave equation, or BBM-equation
u_t + u_x + uu_x-u_xxt = 0 (2)
are formal reductions of the full, two-dimensional Euler equations for free surface flow. This
talk is concerned with the two-point boundary value problem for (1) and (2) wherein the wave
motion is specified at both ends of a finite stretch of length L of the media of propagation.
After ascertaining natural boundary specifications that constitute well posed problems, it is
shown that the solution of the two-point boundary value problem, posed on the interval [0;L],
say, converges as L converges to infinity, to the solution of the quarter-plane boundary value problem in
which a semi-infinite stretch [0;1) of the medium is disturbed at its finite end (the so-called
wavemaker problem). In addition to its intrinsic interest, our results provide justification for the use of the
two-point boundary-value problem in numerical studies of the quarter plane problem for
both the KdV-equation and the BBM-equation.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, October 21, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Klas Udekwu – Biology, Emory University – ikeche@gmail.com

Treatment of bacterial
infections with antibiotics is universally accepted as one of (if not THE) most
significant contributions of medical intervention to reducing mortality and
morbidity during last century. Surprisingly, basic knowledge about how
antibiotics kill or prevent the growth of bacteria is only just beginning to
emerge and the dose and term of antibiotic treatment has long been determined
by clinicians empirically and intuitively.
There is a recent drive to
theoretically and experimentally rationalize antibiotic treatment protocols with
the aim to them and to design protocols which maximize antibiotics’ efficacy
while preventing resistance emergence. Central to these endeavors are the
pharmacodynamics of the antibiotic(s) and bacteria, PD (the relationship
between the concentration of the antibiotic and the rate of growth/death of
bacteria), and the pharmacokinetics of the antibiotic, PK (the distribution and
change in concentration of the antibiotics in a treated host) of each
bacteria. The procedures for
estimating of PD and PK parameters are well established and standardized
worldwide. Although different PK
parameters are commonly employed for the design of antibiotic treatment
protocols most of these considerations, a single PD parameter is usually used,
the minimum inhibitory concentration (MIC). The Clinical and Laboratory
Standards Institute (CLSI)
approved method for estimating MICs defines testing conditions that are optimal
for the antibiotic, like low densities and exponential growth, rarely obtain
outside of the laboratory and virtually never in the bacteria infecting
mammalian hosts. Real
infections with clinical symptoms commonly involve very high densities of
bacteria, most of which are not replicating, and these bacteria are rarely
planktonic, rather residing as colonies or within matrices called biofilms
which sometimes include other species of bacteria. Refractoriness (non-inherited resistance) is the term used to
describe an observed inefficacy of antibiotics on otherwise
antibiotic-susceptible bacterial populations. This talk will focus on our
efforts to describe the pharmacodynamic relationship between Staphylococcus
aureus and antibiotics of six
classes in the light of antibiotic refractoriness.
I will begin by addressing
the effects of cell density on the MIC index, after which I intend to present
unpublished data descriptive of physiology-related effects on antibiotic
efficacy. Additionally, we will explore
the potential contribution of such in vitro results, to observed/predicted clinical
outcomes using standard mathematical models of antibiotic treatment which also
serve to generate testable hypotheses.

- Series
- Research Horizons Seminar
- Time
- Wednesday, October 21, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 171
- Speaker
- Doron Lubinsky – School of Mathematics, Georgia Tech – Lubinsky@math.gatech.edu

Orthogonal polynomials are an important tool in many areas of pure and
applied mathematics. We outline one application in random matrix
theory. We discuss generalizations of orthogonal polynomials such as
the Muntz orthogonal polynomials investigated by Ulfar Stefansson.
Finally, we present some conjectures about biorthogonal polynomials,
which would be a great Ph.D. project for any interested student.

- Series
- Other Talks
- Time
- Wednesday, October 21, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Farbod Shokrieh – Ga Tech

As we have seen already, the global section functor is left exact. To get a long exact sequence, I will first give the construction of derived functors in the more general setting of abelian categories withenough injectives. If time permits, I will then show that for any ringed space the category of all sheaves of Modules is an abelian category with enough injectives, and so we can construct sheaf cohomology as the right derived functors of the global section functor. The relation with Cech cohomology will be studied in a subsequent talk.

- Series
- Analysis Seminar
- Time
- Wednesday, October 21, 2009 - 14:00 for 8 hours (full day)
- Location
- Skiles 269
- Speaker
- Yuliya Babenko – Sam Houston State University

In this talk we will discuss Kolmogorov and Landau type inequalities for the derivatives. These are the inequalities which estimate the norm of the intermediate
derivative of a function (defined on an interval, R_+, R, or
their multivariate analogs) from some class in terms of the norm of the
function itself and norm of its highest derivative.
We shall present several new results on sharp inequalities of this type
for special classes of functions (multiply monotone and absolutely
monotone) and sequences. We will also highlight some of the techniques
involved in the proofs (comparison theorems) and discuss several
applications.

- Series
- Other Talks
- Time
- Wednesday, October 21, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Klaus, Room 1116
- Speaker
- Ravi Kannan – Microsoft Research Labs, Bangalore India

Tea and light refreshments 1:30 in Room 2222. Organizer: Santosh Vempala

Concentration results for the TSP, MWST and many other problems with random inputs show the answer is concentrated tightly around the mean. But most results assume uniform density of the input. We will generalize these to heavy-tailed inputs which seem to be ubiquitous in modern applications. To accomplish this, we prove two new general probability inequalities. The simpler first inequality weakens both hypotheses in Hoffding-Azuma inequality and is enough to tackle TSP, MWST and Random Projections. The second inequality further weakens the moment requirements and using it, we prove the best possible concentration for the long-studied bin packing problem as well as some others. Many other applications seem possible..

- Series
- School of Mathematics Colloquium
- Time
- Thursday, October 22, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Jerry Bona – University of Illinois at Chicago

After a brief account of some of
the history of this classical subject,
we indicate how such models are derived.
Rigorous theory justifying the models
will be discussed and the conversation
will then turn to some applications.
These will be drawn from questions
arising in geophysics and coastal
engineering, as time permits.

- Series
- Graph Theory Seminar
- Time
- Thursday, October 22, 2009 - 12:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Peter Whalen – Math, GT

The Jacobian of a graph, also known as the Picard Group, Sandpile Group, or Critical Group, is a discrete analogue of the Jacobian of an algebraic curve. It is known that the order of the Jacobian of a graph is equal to its number of spanning trees, but the exact structure is known for only a few classes of graphs. In this talk I will present a combinatorial method of approaching the Jacobian of graphs by way of a chip-firing game played on its vertices. We then apply this chip-firing game to explicitly characterize the Jacobian of nearly complete graphs, those obtained from the complete graph by deleting either a cycle or two vertex-disjoint paths incident with all but one vertex. This is joint work with Sergey Norin.

- Series
- Stochastics Seminar
- Time
- Thursday, October 22, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Ton Dieker – (ISyE, Georgia Tech)

In this talk, we study an interacting particle system arising in the
context of series Jackson queueing networks. Using effectively nothing
more than the Cauchy-Binet identity, which is a standard tool in
random-matrix theory, we show that its transition probabilities can be
written as a signed sum of non-crossing probabilities. Thus, questions
on time-dependent queueing behavior are translated to questions on
non-crossing probabilities. To illustrate the use of this connection,
we prove that the relaxation time (i.e., the reciprocal of the
’spectral gap’) of a positive recurrent system equals the relaxation
time of a single M/M/1 queue with the same arrival and service rates as
the network’s bottleneck station. This resolves a 1985 conjecture from
Blanc on series Jackson networks.
Joint work with Jon Warren, University of Warwick.

- Series
- Analysis Seminar
- Time
- Friday, October 23, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Doug Hardin – Vanderbilt University

I will review recent and classical results concerning the
asymptotic properties (as N --> \infty) of 'ground state' configurations
of N particles restricted to a d-dimensional compact set A\subset {\bf R}^p
that minimize the Riesz s-energy functional
\sum_{i\neq j}\frac{1}{|x_{i}-x_{j}|^{s}}
for s>0.
Specifically, we will discuss the following
(1) For s < d, the ground state configurations have limit distribution as
N --> \infty given by the equilibrium measure \mu_s, while the first
order asymptotic growth of the energy of these configurations is given by
the 'transfinite diameter' of A.
(2) We study the behavior of \mu_s as s approaches the critical
value d (for s\ge d, there is no equilibrium measure). In the case that
A is a fractal, the notion of 'order two density' introduced by Bedford
and Fisher naturally arises. This is joint work with M. Calef.
(3) As s --> \infty, ground state configurations approach best-packing
configurations on A. In work with S. Borodachov and E. Saff we show that
such configurations are asymptotically uniformly distributed on A.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, October 23, 2009 - 15:00 for 2 hours
- Location
- Skiles 269
- Speaker
- Amey Kaloti – Georgia Tech

This is a 2 hour talk.

Abstract: Heegaard floer homology is an invariant of closed 3 manifolds defined by Peter
Ozsvath and Zoltan Szabo. It has proven to be a very strong invariant of 3 manifolds with
connections to contact topology. In these talks we will try to define the Heegaard Floer
homology without assuming much background in low dimensional topology. One more goal is
to present the combinatorial description for this theory.

- Series
- ACO Seminar
- Time
- Friday, October 23, 2009 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Eyal Lubetzky – Microsoft Research, Redmond, WA

The class of random regular graphs has been the focus of extensive study highlighting
the excellent expansion properties of its typical instance. For instance, it is well
known that almost every regular graph of fixed degree is essentially Ramanujan, and
understanding this class of graphs sheds light on the general behavior of expanders.
In this talk we will present several recent results on random regular graphs,
focusing on the interplay between their spectrum and geometry.
We will first discuss the relation between spectral properties and the abrupt
convergence of the simple random walk to equilibrium, derived from precise
asymptotics of the number of paths between vertices. Following the study of the graph
geometry we proceed to its random perturbation via exponential weights on the edges
(first-passage-percolation). We then show how this allows the derivation of various
properties of the classical Erd\H{o}s-R\'enyi random graph near criticality. Finally,
returning to the spectrum of random regular graph, we discuss the question of how
close they really are to being Ramanujan and conclude with related problems involving
random matrices.
Based on joint works with Jian Ding, Jeong Han Kim and Yuval Peres, with Allan Sly
and with Benny Sudakov and Van Vu.

- Series
- Probability Working Seminar
- Time
- Friday, October 23, 2009 - 16:00 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 154
- Speaker
- Tobias Hurth – Georgia Tech

The talk is based on a 1992 paper by Yakov Sinai. He proves a localization property for random walks in the random potential known as Nechaev's model.

- Series
- Other Talks
- Time
- Saturday, October 24, 2009 - 12:30 for 2 hours
- Location
- LeCraw Auditorium
- Speaker
- Richard Karp – Electrical Engineering and Computer Sciences, University of California, Berkeley

From time to time a new algorithm comes along that causes a sensation in theoretical computer science or in an area of application because of its resolution of a long-standing open question, its surprising efficiency, its practical usefulness, the novelty of its setting or approach, the elegance of its structure, the subtlety of its analysis or its range of applications. We will give examples of algorithms that qualify for greatness for one or more of these reasons, and discuss how to equip students to appreciate them and understand their strengths and weaknesses.

- Series
- Other Talks
- Time
- Saturday, October 24, 2009 - 13:50 for 3 hours
- Location
- LeCraw Auditorium
- Speaker
- Mihalis Yannakakis – Computer Science, Columbia University

Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; price equilibria in markets; optimal strategies and the values of competitive games (stochastic and other games); stable configurations of neural networks; analysis of the evolution of various types of dynamic stochastic models. It is not known whether these problems can be solved in polynomial time. Despite their broad diversity, there are certain common computational principles that underlie different types of equilibria and connect many of these problems to each other. In this talk we will discuss some of these common principles and the corresponding complexity classes that capture them; the effect on the complexity of the underlying computational framework; and the relationship with other open questions in computation.

- Series
- Other Talks
- Time
- Saturday, October 24, 2009 - 15:10 for 1.5 hours (actually 80 minutes)
- Location
- LeCraw Auditorium
- Speaker
- Noga Alon – Mathematics and Computer Science, Tel Aviv University

The spectral properties of a graph are intimately related to its structure. This can be applied in the study of discrete isoperimetric problems and in the investigation of extremal and algorithmic questions for graphs. I will discuss several recent examples illustrating this theme.

- Series
- ACO Distinguished Lecture
- Time
- Saturday, October 24, 2009 - 17:00 for 1 hour (actually 50 minutes)
- Location
- LeCraw Auditorium, College of Management
- Speaker
- Manuel Blum – Computer Science, Carnegie Mellon University

Preceded with a reception at 4:10pm.

To come to grips with consciousness, I postulate that living entities in
general, and human beings in particular, are mechanisms... marvelous
mechanisms to be sure but not magical ones... just mechanisms. On this
basis, I look to explain some of the paradoxes of consciousness such as
Samuel Johnson's "All theory is against the freedom of the will; all
experience is for it."
I will explain concepts of self-awareness and free will from a mechanistic
view. My explanations make use of computer science and suggest why these
phenomena would exist even in a completely deterministic world. This is
particularly striking for free will.
The impressions of our senses, like the sense of the color blue, the sound
of a tone, etc. are to be expected of a mechanism with enormously many
inputs categorized into similarity classes of sight, sound, etc. Other
phenomena such as the "bite" of pain are works in progress. I show the
direction that my thinking takes and say something about what I've found and
what I'm still looking for. Fortunately, the sciences are discovering a
great deal about the brain, and their discoveries help enormously in guiding
and verifying the results of this work.

- Series
- Geometry Topology Working Seminar
- Time
- Monday, October 26, 2009 - 10:00 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Shea Vela-Vick – Columbia University

We will focus on the "toy model" of bordered Floer homology. Loosely speaking, this is bordered Floer homology for grid diagrams of knots. While the toy model unfortunately does not provide us with any knot invariants, it highlights many of the key ideas needed to understand the more general theory.
Note the different time and place!
This is a 1.5 hour talk.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, October 26, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Chiu-Yen Kao – Ohio State University (Department of Mathematics) – kao@math.ohio-state.edu

The Kadomtsev-Petviashvili (KP) equation is a two-dimensional dispersivewave equation which was proposed to study the stability of one solitonsolution of the KdV equation under the influence of weak transversalperturbations. It is well know that some closed-form solutions can beobtained by function which have a Wronskian determinant form. It is ofinterest to study KP with an arbitrary initial condition and see whetherthe solution converges to any closed-form solution asymptotically. Toreveal the answer to this question both numerically and theoretically, weconsider different types of initial conditions, including one-linesoliton, V-shape wave and cross-shape wave, and investigate the behaviorof solutions asymptotically. We provides a detail description ofclassification on the results. The challenge of numerical approach comes from the unbounded domain andunvanished solutions in the infinity. In order to do numerical computationon the finite domain, boundary conditions need to be imposed carefully.Due to the non-periodic boundary conditions, the standard spectral methodwith Fourier methods involving trigonometric polynomials cannot be used.We proposed a new spectral method with a window technique which will makethe boundary condition periodic and allow the usage of the classicalapproach. We demonstrate the robustness and efficiency of our methodsthrough numerous simulations.

- Series
- Geometry Topology Seminar
- Time
- Monday, October 26, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Shea Vela-Vick – Columbia University

To each three-component link in the 3-dimensional sphere we associate a characteristic map from the 3-torus to the 2-sphere, and establish a correspondence between the pairwise and Milnor triple linking numbers of the link and the Pontryagin invariants that classify its characteristic map up to homotopy. This can be viewed as a natural extension of the familiar fact that the linking number of a two-component link is the degree of its associated Gauss map from the 2-torus to the 2-sphere.In the case where the pairwise linking numbers are all zero, I will present an integral formula for the triple linking number analogous to the Gauss integral for the pairwise linking numbers. The integrand in this formula is geometrically natural in the sense that it is invariant under orientation-preserving rigid motions of the 3-sphere.

- Series
- Stelson Lecture Series
- Time
- Monday, October 26, 2009 - 16:00 for 1 hour (actually 50 minutes)
- Location
- SST Room 2
- Speaker
- Thomas Y. Hou – California Institute of Technology, Applied and Computational Mathematics

This lecture is more for the general audience. Reception following lecture. Organizers: Chongchun Zeng and Hao Min Zhou

Many problems of fundamental and practical importance contain multiple scale solutions. Composite and nano materials, flow and transport in heterogeneous porous media, and turbulent flow are examples of this type. Direct numerical simulations of these multiscale problems are extremely difficult due to the wide range of length scales in the underlying physical problems. Direct numerical simulations using a fine grid are very expensive. Developing effective multiscale methods that can capture accurately the large scale solution on a coarse grid has become essential in many engineering applications. In this talk, I will use two examples to illustrate how multiscale mathematics analysis can impact engineering applications. The first example is to develop multiscale computational methods to upscale multi-phase flows in strongly heterogeneous porous media. Multi-phase flows arise in many applications, ranging from petroleum engineering, contaminant transport, and fluid dynamics applications. Multiscale computational methods guided by multiscale analysis have already been adopted by the industry in their flow simulators. In the second example, we will show how to develop a systematic multiscale analysis for incompressible flows in three space dimensions. Deriving a reliable turbulent model has a significant impact in many engineering applications, including the aircraft design. This is known to be an extremely challenging problem. So far, most of the existing turbulent models are based on heuristic closure assumption and involve unknown parameters which need to be fitted by experimental data. We will show that how multiscale analysis can be used to develop a systematic multiscale method that does not involve any closure assumption and there are no adjustable parameters.

- Series
- Stelson Lecture Series
- Time
- Tuesday, October 27, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Thomas Y. Hou – California Institute of Technology, Applied and Computational Mathematics

This lecture will be more for the mathematical audience

Whether the 3D incompressible Navier-Stokes equations can develop
a finite time singularity from smooth initial data is one of the
seven Millennium Problems posted by the Clay Mathematical Institute.
We review some recent theoretical and computational studies of the
3D Euler equations which show that there is a subtle dynamic depletion of
nonlinear vortex stretching due to local geometric regularity of
vortex filaments. The local geometric regularity of vortex filaments
can lead to tremendous cancellation of nonlinear vortex stretching.
This is also confirmed by our large scale computations for some of
the most well-known blow-up candidates. We also
investigate the stabilizing effect of convection in 3D incompressible
Euler and Navier-Stokes equations. The convection term is the main source
of nonlinearity for these equations. It is often considered destabilizing
although it conserves energy due to the incompressibility condition. Here
we reveal a surprising nonlinear stabilizing effect that the convection
term plays in regularizing the solution. Finally, we present a new class
of solutions for the 3D Euler and Navier-Stokes equations, which exhibit
very interesting dynamic growth property. By exploiting the special
structure of the solution and the cancellation between the convection
term and the vortex stretching term, we prove nonlinear stability and
the global regularity of this class of solutions.

- Series
- Dissertation Defense
- Time
- Tuesday, October 27, 2009 - 13:30 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 269
- Speaker
- Selma Yildirim-Yolcu – School of Mathematics, Georgia Tech

In this thesis, some eigenvalue inequalities for Klein-Gordon operators and restricted to a bounded domain in Rd are proved. Such operators become very popular recently as they arise in many problems ranges from mathematical finance to crystal dislocations, especially the relativistic quantum mechanics and \alpha-stable stochastic processes. Many of the results obtained here concern finding bounds for some spectral functions of these operators. The subject, which is well developed for the Laplacian, is examined from the spectral theory perspective through some of the tools used to prove analogues results for the Laplacian. This work highlights some important results, sparking interest in constructing a similar theory for Klein-Gordon operators. For instance, the Weyl asymptotics and semiclassical bounds for the operator Hm, are developed. As a result, a Berezin-Li-Yau type inequality is derived and an improvement of the bound is proved.

- Series
- Mathematical Finance/Financial Engineering Seminar
- Time
- Tuesday, October 27, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Piotr Kokoszka – Utah State University

The functional autoregressive process
has become a useful tool in the analysis of functional time series
data. In this model, the observations and the errors are curves,
and the role of the autoregressive coefficient is played by
an integral operator.
To ensure meaningful inference and prediction,
it is important to verify that this operator
does not change with time. We propose a method for testing
its constancy which uses the
functional principal component analysis. The test statistic is
constructed to have a Kiefer type asymptotic distribution. The
asymptotic justification of the procedure is very delicate and
touches upon central notions of functional data analysis.
The test is implemented using the
R package fda. Its finite sample performance is
illustrated by an application to credit card transaction data.

- Series
- PDE Seminar
- Time
- Tuesday, October 27, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Dongho Chae – Sungkyunkwan University, Korea and Universty of Chicago

We first discuss blow-up rates and the blow-up profiles of possible asymptotically self-similar singularities of the 3D Euler equations,
where the sense of convergence and self-similarity are considered in various sense. We extend much further, in particular, the previous nonexistence results of self-similar/asymptotically self-similar singularities. In the second part of the talk we discuss some observations on the Euler equations with symmetries, which shows that the point-wise behavior of the pressure along the flows is closely related to the blow-up of of solutions.

- Series
- Geometry Topology Working Seminar
- Time
- Wednesday, October 28, 2009 - 10:00 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Shea Vela-Vick – Columbia University

Here we will introduce the basic definitions of bordered Floer homology. We will discuss bordered Heegaard diagrams as well as the algebraic objects, like A_\infinity algebras and modules, involved in the theory. We will also discuss the pairing theorem which states that if Y = Y_1 U_\phi Y_2 is obtained by identifying the (connected) boundaries of Y_1 and Y_2, then the closed Heegaard Floer theory of Y can be obtained as a suitable tensor product of the bordered theories of Y_1 and Y_2.Note the different time and place!This is a 1.5 hour talk.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, October 28, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Troy Shinbrot – Biomedical Engineering, Rutgers University

Many vertebrate motor and sensory systems "decussate," or cross the
midline to the opposite side of the body. The successful crossing of
millions of axons during development requires a complex of tightly
controlled regulatory processes. Since these processes have evolved
in many distinct systems and organisms, it seems reasonable to
presume that decussation confers a significant functional advantage -
yet if this is so, the nature of this advantage is not understood.
In this talk, we examine constraints imposed by topology on the ways
that a three dimensional processor and environment can be wired
together in a continuous, somatotopic, way. We show that as the
number of wiring connections grows, decussated arrangements become
overwhelmingly more robust against wiring errors than seemingly
simpler same-sided wiring schemes. These results provide a
predictive approach for understanding how 3D networks must be wired
if they are to be robust, and therefore have implications both
regenerative strategies following spinal injury and for future large
scale computational networks.

- Series
- Other Talks
- Time
- Wednesday, October 28, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- ISyE Executive Classroom
- Speaker
- Pushkar Tripathi – ACO, Computing Science and Systems, Georgia Tech

Organizer: Daniel Dadush, ACO Student, ISyE

Applications in complex systems such as the Internet have spawned recent interest in studying situations involving multiple agents with their individual cost or utility functions. We introduce an algorithmic framework for studying combinatorial problems in the presence of multiple agents with submodular cost functions. We study several fundamental covering problems (Vertex Cover, Shortest Path, Perfect Matching, and Spanning Tree) in this setting and establish tight upper and lower bounds for the approximability of these problems. This talk is based on joint work with Gagan Goel, Chinmay Karande and Wang Lei. This is a joint ACO/DOS seminar, so please come a little early for pizza and refreshments sponsored by ACO.

- Series
- Research Horizons Seminar
- Time
- Wednesday, October 28, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 171
- Speaker
- Igor Belegradek – School of Mathematics, Georgia Tech – ib@math.gatech.edu

The Soul Theorem, proved by Cheeger and Gromoll forty
year ago, reveals a beautiful structure of noncompact complete
manifolds of nonnegative curvature. In the talk I will sketch
a proof of the Soul Theorem, and relate it to my current work
on moduli spaces of nonnegatively curved metrics.

- Series
- Analysis Seminar
- Time
- Wednesday, October 28, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Mrinal Ragupathi – Vanderbilt University

Given points $z_1,\ldots,z_n$ on a finite open Riemann
surface $R$ and complex scalars $w_1,\ldots,w_n$, the Nevanlinna-Pick
problem is to determine conditions for the existence of a holomorphic
map $f:R\to \mathbb{D}$ such that $f(z_i) = w_i$.
In this talk I will provide some background on the problem, and then
discuss the extremal case. We will try to discuss how a method of
McCullough can be used to provide more qualitative information about
the solution. In particular, we will show that extremal cases are
precisely the ones for which the solution is unique.

- Series
- Geometry Topology Seminar
- Time
- Wednesday, October 28, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Roland van der Veen – University of Amsterdam – r.i.vanderveen@uva.nl

We recall the Schur Weyl duality from representation theory and show how this can be applied to express the colored Jones polynomial of torus knots in an elegant way. We'll then discuss some applications and further extensions of this method.

- Series
- Joint ACO and ARC Colloquium
- Time
- Thursday, October 29, 2009 - 11:05 for 1 hour (actually 50 minutes)
- Location
- MiRC 102
- Speaker
- Anna Gilbert – Mathematics, University of Michigan

The past 10 years have seen a confluence of research in sparse approximation
amongst computer science, mathematics, and electrical engineering.
Sparse approximation
encompasses a large number of mathematical, algorithmic, and signal
processing problems which all attempt to balance the size of a (linear)
representation of data and the fidelity of that representation. I will
discuss several of the basic algorithmic problems and their solutions,
including connections to streaming algorithms and compressive sensing.

- Series
- SIAM Student Seminar
- Time
- Friday, October 30, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Ulfar Stefansson – School of Mathematics, Georgia Tech

After a brief introduction of the theory of orthogonal polynomials, where we touch on some history and applications, we present results on Müntz orthogonal polynomials. Müntz polynomials arise from consideration of the Müntz Theorem, which is a beautiful generalization of the Weierstrass Theorem. We prove a new surprisingly simple representation for the Müntz orthogonal polynomials which holds on the interval of orthogonality, and in particular we get new formulas for some of the classical orthogonal polynomials (e.g. Legendre, Jacobi, Laguerre). This allows us to determine the strong asymptotics on the interval, and the zero spacing behavior follows. We also look at the asymptotic behavior outside the interval, where we apply the method of stationary phase.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, October 30, 2009 - 15:00 for 2 hours
- Location
- Skiles 269
- Speaker
- Shea Vela-Vick – Columbia University

In this talk I will discuss a generalizations and/oo applications of bordered Floer homology. After reviewing the basic definitions and constructions, I will focus either on an application to sutured Floer homology developed by Rumen Zarev, or on applications of the theory to the knot Floer homology. (While it would be good to have attended the other two talks this week, this talk shoudl be independent of them.) This is a 2 hour talk.

- Series
- Graph Theory Seminar
- Time
- Friday, October 30, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Asaf Shapira – Math and CS, GT

A graph G is k-critical if every proper subgraph of G is (k-1)-colorable, but the graph G itself is not. We prove that every k-critical graph on n vertices has a cycle of length at least logn/100logk, improving a bound of Alon, Krivelevich and Seymour from 2000. Examples of Gallai from 1963 show that this bound is tight (up to a constant depending on k). We thus settle the problem of bounding the minimal circumference of k-critical graphs, raised by Dirac in 1952 and Kelly and Kelly in 1954. This is joint work with Robin Thomas.

- Series
- CDSNS Colloquium
- Time
- Monday, November 2, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Wen Huang – USTC, China and SoM, Georgia Tech

Stable sets and unstable sets of a dynamical system with positive entropy
are investigated. It is shown that in any invertible system with positive entropy,
there is a measure-theoretically ?rather big? set such that for any point from the
set, the intersection of the closure of the stable set and the closure of the
unstable set of the point has positive entropy.
Moreover, for several kinds of specific systems, the lower bound of Hausdorff
dimension of these sets is estimated. Particularly the lower bound of the Hausdorff
dimension of such sets appearing in a positive entropy diffeomorphism on a smooth
Riemannian manifold is given in terms of the metric entropy and of Lyapunov exponent.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, November 2, 2009 - 13:00 for 30 minutes
- Location
- Skiles 255
- Speaker
- Rustum Choksi – Simon Fraser University

A density functional theory of Ohta and Kawasaki gives rise to nonlocal perturbations of the well-studied Cahn-Hilliard and isoperimetric variational problems. In this talk, I will discuss these simple but rich variational problems in the context of diblock copolymers. Via a combination of rigorous analysis and numerical simulations, I will attempt to characterize minimizers without any preassigned bias for their geometry.

Energy-driven pattern formation induced by competing short and long-range interactions is ubiquitous in science, and provides a source of many challenging problems in nonlinear analysis. One example is self-assembly of diblock copolymers. Phase separation of the distinct but bonded chains in dibock copolymers gives rise to an amazingly rich class of nanostructures which allow for the synthesis of materials with tailor made mechanical, chemical and electrical properties. Thus one of the main challenges is to describe and predict the self-assembled nanostructure given a set of material parameters.

- Series
- Analysis Working Seminar
- Time
- Monday, November 2, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Brett Wick – Georgia Tech

We continue our study of Seip's Interpolation Theorem in weighted Bergman spaces. This lecture should cover the necessary direction in the characterization of the Theorem.

- Series
- Joint ACO and ARC Colloquium
- Time
- Monday, November 2, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Klaus 1116W
- Speaker
- Alexander Barvinok – University of Michigan

Tea and light refreshments 1:30 in Room 2222. Organizer: Santosh Vempala

I will discuss recent progress on the construction of randomized algorithms for counting non-negative integer matrices with prescribed row and column sums and on finding asymptotic formulas for the number of such matrices (also known as contingency tables). I will also discuss what a random (with respect to the uniform measure) non-negative integer matrix with prescribed row and column sums looks like.

- Series
- Mathematical Finance/Financial Engineering Seminar
- Time
- Tuesday, November 3, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Sheldon Lin – Department of Statistics, University of Toronto

The discounted penalty function proposed in the seminal paper
Gerber and Shiu (1998) has been widely used to
analyze the time of ruin,
the surplus immediately before ruin and the deficit at ruin
of insurance risk models in ruin theory.
However, few of its applications can be found beyond,
except that Gerber and Landry (1998)
explored its use for the pricing of perpetual American put options. In
this talk,
I will discuss the use of the discounted penalty function and mathematical
tools
developed for the function
for perpetual American catastrophe
put options. Assuming that catastrophe losses
follow a mixture of Erlang distributions,
I will show that an analytical (semi-closed) expression for the price of
perpetual American catastrophe put options can be obtained.
I will then discuss
the fitting of a mixture of Erlang distributions to catastrophe loss
data using an EM algorithm.

- Series
- PDE Seminar
- Time
- Tuesday, November 3, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Qing Han – University of Notre Dame

We prove a conjecture of Bryant, Griffiths, and Yang concerning the characteristic variety for the determined isometric embedding system. In particular, we show that the characteristic variety is not smooth for any dimension greater than 3. This is accomplished by introducing a smaller yet equivalent linearized system, in an appropriate way, which facilitates analysis of the characteristic variety.

- Series
- Stochastics Seminar
- Time
- Tuesday, November 3, 2009 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255 (Note unusual time and location)
- Speaker
- Ivan NOURDIN – Paris VI

My aim is to explain how to prove multi-dimensional central limit
theorems for the spectral moments (of arbitrary degrees) associated with
random matrices with real-valued i.i.d. entries, satisfying some appropriate
moment conditions. The techniques I will use rely on a universality
principle for the Gaussian Wiener chaos as well as some combinatorial
estimates. Unlike other related results in the probabilistic literature, I
will not require that the law of the entries has a density with respect to
the Lebesgue measure.
The talk is based on a joint work with Giovanni Peccati, and use an
invariance principle obtained in a joint work with G. P. and Gesine
Reinert

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, November 4, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Tanya Berger-Wolf – Department of Computer Science, University of Illinois at Chicago

Computation has fundamentally changed the way we study nature. Recent breakthroughs in data collection technology, such as GPS and other mobile sensors, are giving biologists access to data about wild populations that are orders of magnitude richer than any previously collected. Such data offer the promise of answering some of the big ecological questions about animal populations. The data are not unique to animal domain but is now prevalent in human interactions: emails, blogs, and online social networks. Unfortunately, our ability to analyze these data lags substantially behind our ability to collect it. In particular, interactions among individuals are often modeled as social networks where nodes represent individuals and an edge exists if the corresponding individuals have interacted during the observation period. The model is essentially static in that the interactions are aggregated over time and all information about the time and ordering of social interactions is discarded. We show that suchtraditional social network analysis methods may result in incorrect conclusions on dynamic data about the structure of interactions and the processes that spread over those interactions. We have extended computational methods for social network analysis to explicitly address the dynamic nature of interactions among individuals. We have developed techniques for identifying persistent communities, influential individuals, and extracting patterns of interactions in dynamic social networks. We will present our approach and demonstrate its applicability by analyzing interactions among zebra populations.

- Series
- Research Horizons Seminar
- Time
- Wednesday, November 4, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 171
- Speaker
- Leonid Bunimovich – School of Mathematics, Georgia Tech – bunimovh@math.gatech.edu

Dynamical systems theory is concerned with systems that change in time
(where time can be any semigroup). However, it is quite rare that one
can find the solutions for such systems or even a "sizable" subset of
such solutions. An approach motivated by this fact, that goes back to
Poincaré, is to study instead partitions of the (phase) space M of all
states of a dynamical system and consider the evolution of the elements
of this partition (instead of the evolution of points of M).
I'll explain how the objects in the title appear, some relations between
them, and formulate a few general as well as more specific open problems
suitable for a PhD thesis in dynamical systems, mathematical biology,
graph theory and applied and computational mathematics.
This talk will also serve to motivate and introduce to the topics to be
given in tomorrow's colloquium.

- Series
- Other Talks
- Time
- Wednesday, November 4, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Farbod Shokrieh – Ga Tech

We will continue the study of derived functors between abelian categories. I will show why injective objects are needed for the construction. I will then show that, for any ringed space, the abelian category of all sheaves of Modules has enough injectives. The relation with Cech cohomology will also be studied.

- Series
- Analysis Seminar
- Time
- Wednesday, November 4, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Dr Carlos Villegas Blas – Instituto de Matematicas UNAM, Unidad. Cuernavaca – villegas@matcuer.unam.mx

We will introduce a Bargmann transform from the space of square integrable functions on the n-sphere onto a suitable Hilbert space of holomorphic functions on a null quadric. On base of our Bargmann transform, we will introduce a set of coherent states and study their semiclassical properties. For the particular cases n=2,3,5, we will show the relation with two known regularizations of the Kepler problem: the Kustaanheimo-Stiefel and Moser regularizations.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, November 5, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Lyonia Bunimovich – Georgia Tech

Real life networks are usually large and have a very complicated
structure. It is tempting therefore to simplify or reduce the associated
graph of interactions in a network while maintaining its basic structure
as well
as some characteristic(s) of the original graph. A key question is which
characteristic(s) to conserve while reducing a graph. Studies of
dynamical networks reveal that an important characteristic of a
network's structure is a spectrum of its adjacency matrix.
In this talk we present an approach which allows for the reduction of
a general
weighted graph in such a way that the spectrum of the graph's (weighted)
adjacency matrix is maintained up to some finite set that is known in
advance. (Here, the possible weights belong to the set of complex
rational functions, i.e. to a very general class of weights).
A graph can be isospectrally reduced to a graph on any subset of its
nodes, which could be an important property for various applications. It
is also possible to introduce a new equivalence relation in the set of
all networks. Namely, two networks are spectrally equivalent if each of
them can be isospectrally reduced onto one and the same (smaller) graph.
This result should also be useful for analysis of real networks.
As the first application of the isospectral graph reduction we
considered a problem of estimation of spectra of matrices. It happens
that our procedure allows for improvements of the estimates obtained by
all three classical methods given by Gershgorin, Brauer and Brualdi.
(Joint work with B.Webb)
A talk will be readily accessible to undergraduates familiar with
matrices and complex functions.

- Series
- Stochastics Seminar
- Time
- Thursday, November 5, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Vlad Vysotsky – University of Delaware

Let $S_n$ be a centered random walk with a finite variance, and define the new sequence
$\sum_{i=1}^n S_i$, which we call the {\it integrated random walk}. We are interested in
the asymptotics of $$p_N:=\P \Bigl \{ \min \limits_{1 \le k \le N} \sum_{i=1}^k S_i \ge
0 \Bigr \}$$ as $N \to \infty$. Sinai (1992) proved that $p_N \asymp N^{-1/4}$ if $S_n$
is a simple random walk. We show that $p_N \asymp N^{-1/4}$ for some other types of
random walks that include double-sided exponential and double-sided geometric walks (not
necessarily symmetric). We also prove that $p_N \le c N^{-1/4}$ for lattice walks and
upper exponential walks, i.e., walks such that $\mbox{Law} (S_1 | S_1>0)$ is an
exponential distribution.

- Series
- SIAM Student Seminar
- Time
- Friday, November 6, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Mitch Keller – School of Mathematics, Georgia Tech

Suppose that Amtrak runs a train from Miami, Florida, to Bangor, Maine. The train makes stops at many locations along the way to drop off passengers and pick up new ones. The computer system that sells seats on the train wants to use the smallest number of seats possible to transport the passengers along the route. If the computer knew before it made any seat assignments when all the passengers would get on and off, this would be an easy task. However, passengers must be given seat assignments when they buy their tickets, and tickets are sold over a period of many weeks. The computer system must use an online algorithm to make seat assignments in this case, meaning it can use only the information it knows up to that point and cannot change seat assignments for passengers who purchased tickets earlier. In this situation, the computer cannot guarantee it will use the smallest number of seats possible. However, we are able to bound the number of seats the algorithm will use as a linear function of the minimum number of seats that could be used if assignments were made after all passengers had bought their tickets. In this talk, we'll formulate this problem as a question involving coloring interval graphs and discuss online algorithms for other questions on graphs and posets. We'll introduce or review the needed concepts from graph theory and posets as they arise, minimizing the background knowledge required.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, November 6, 2009 - 15:00 for 2 hours
- Location
- Skiles 269
- Speaker
- Meredith Casey – Georgia Tech

The goal of this talk is to describe simple constructions by which we can construct any compact, orientable 3-manifold. It is well-known that every orientable 3-manifold has a Heegaard splitting. We will first define Heegaard splittings, see some examples, and go through a very geometric proof of this therem. We will then focus on the Dehn-Lickorish Theorem, which states that any orientation-preserving homeomorphism of an oriented 2-manifold without boundary can by presented as the composition of Dehn twists and homeomorphisms isotopic to the identity. We will prove this theorm, and then see some applications and examples. With both of these resutls together, we will have shown that using only handlebodies and Dehn twists one can construct any compact, oriented 3-manifold.

- Series
- Other Talks
- Time
- Friday, November 6, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 154
- Speaker
- Sergio Almada – Georgia Tech

We consider the Stochastic Differential Equation
$dX_\epsilon=b(X_\epsilon)dt + \epsilon dW$ . Given a domain D, we
study how the exit time and the distribution of the process at the time
it exits D behave as \epsilon goes to 0. In particular, we cover the
case in which the unperturbed system $\frac{d}{dt}x=b(x)$ has a unique
fixed point of the hyperbolic type. We will illustrate how the behavior
of the system is in the linear case. We will remark how our results
give improvements to the study of systems admitting heteroclinic or
homoclinic connections. We will outline the general proof in two
dimensions that requires normal form theory from differential
equations. For higher dimensions, we introduce a new kind of non-smooth
stochastic calculus.

- Series
- Combinatorics Seminar
- Time
- Friday, November 6, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Albert Bush – School of Mathematics, Georgia Tech

This is joint work with Dr. Yi Zhao.

Graph tiling problems can be summarized as follows: given a graph H, what conditions do we need to find a spanning subgraph of some larger graph G that consists entirely of disjoint copies of H. The most familiar example of a graph tiling problem is finding a matching in a graph. With the Regularity Lemma and the Blow-up Lemma as our main tools, we prove a degree condition that guarantees an arbitrary bipartite graph G will be tiled by an arbitrary bipartite graph H. We also prove this degree condition is best possible up to a constant. This answers a question of Zhao and proves an asymptotic version of a result of Kuhn and Osthus for bipartite graphs.

- Series
- CDSNS Colloquium
- Time
- Monday, November 9, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Dongwei Huang – Tianjin Polytechnic University, China and School of Mathematics, Georgia Tech

Many dynamical systems may be subject to stochastic excitations, so to find an efficient method to analyze the stochastic system is very important. As for the complexity of the stochastic systems, there are not any omnipotent methods. What I would like to present here is a brief introduction to quasi-non-integrable Hamiltonian systems and stochastic averaging method for analyzing certain stochastic dynamical systems. At the end, I will give some examples of the method.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, November 9, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Nicola Guglielmi – Università di L&#039;Aquila – guglielm@univaq.it

This is a joint work with Michael Overton (Courant Institute, NYU). The epsilon-pseudospectral abscissa and radius of an n x n matrix are respectively the maximum real part and the maximal modulus of points in its epsilon-pseudospectrum. Existing techniques compute these quantities accurately but the cost is multiple SVDs of order n, which makesthe method suitable to middle size problems. We present a novel approach based on computing only the spectral abscissa or radius or a sequence of matrices, generating a monotonic sequence of lower bounds which, in many but not all cases, converges to the pseudospectral abscissa or radius.

- Series
- Analysis Working Seminar
- Time
- Monday, November 9, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Brett Wick – Georgia Tech

We are going to continue explaining the proof of Seip's Interpolation Theorem for the Bergman Space. We are going to demonstrate the sufficiency of these conditions for a certain example. We then will show how to deduce the full theorem with appropriate modifications of the example.

- Series
- Geometry Topology Seminar
- Time
- Monday, November 9, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Bulent Tosun – Ga Tech

In 3-dimensional contact topology one of the main problem is classifying Legendrian (transverse) knots in certain knot type up to Legendrian ( transverse) isotopy. In particular we want to decide if two (one in case of transverse knots) classical invariants of this knots are complete set of invariants. If it is, then we call this knot type Legendrian (transversely) simple knot type otherwise it is called Legendrian (transversely) non-simple. In this talk, by tracing the techniques developed by Etnyre and Honda, we will present some results concerning the complete Legendrian and transverse classification of certain cabled knots in the standard tight contact 3-sphere. Moreover we will provide an infinite family of Legendrian and transversely non-simple prime knots.

- Series
- PDE Seminar
- Time
- Tuesday, November 10, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Chunjing Xie – University of Michigan, Ann Arbor

In this talk, we will discuss the global existence and asymptotic behavior of classical solutions for two dimensional inviscid Rotating Shallow Water system with small initial data subject to the zero-relative-vorticity constraint. One of the key steps is a reformulation of the problem into a symmetric quasilinear Klein-Gordon system, for which the global existence of classical solutions is then proved with combination of the vector field approach and the normal forms. We also probe the case of general initial data and reveal a lower bound for the lifespan that is almost inversely proportional to the size of the initial relative vorticity. This is joint work with Bin Cheng.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, November 11, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Gennady Cymbalyuk – Georgia State University, Neuroscience Institute and Dept. of Physics and Astronomy

Bursting, tonic spiking, sub-threshold oscillations and silence are basic
robust regimes of activity of a single neuron. The talk will be focused on
the co-existence of regimes of activity of neurons. Such multistability
enhances potential flexibility to the nervous system and has many
implications for motor control and decision making. I will identify
different scenarios leading to multistability in the neuronal dynamics and
discuss its potential roles in the operation of the central nervous system
under normal and pathological conditions.

- Series
- Research Horizons Seminar
- Time
- Wednesday, November 11, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 171
- Speaker
- Jean Bellissard – School of Mathematics, Georgia Tech – jeanbel@math.gatech.edu

An assembly of atoms in a solid phase will be described through the notion
of Delone sets and related to tilings. The Hull and the tiling space wiill
be defined. It will be shown that the tiling space and the Hull can be
constructed through an inverse limit of CW-complexes built out of the
tiles and of the local patches. From then various cohomologies can be
defined and allow to distinguish between these atomic distributions. The
question of whether these topological invariant can be seen in experiments
will be addressed.

- Series
- Other Talks
- Time
- Wednesday, November 11, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Farbod Shokrieh – Ga Tech

We will show that the construction of derived functors satisfy the required universal property.I will then show that, for any ringed space, the abelian category of all sheaves of Modules has enough injectives. We achieve this by first characterizing injective abelian groups (Baer's theorem).The relation with Cech cohomology will also be studied. In particular, I will show that the first Cech and Grothendieck sheaf cohomology groups are isomorphic for any topological space (without using spectral sequences).

- Series
- Analysis Seminar
- Time
- Wednesday, November 11, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Sergiy Borodachov – Towson University

We consider finite systems of contractive homeomorphisms of a complete metric space, which are non-redundanton every level. In general, this condition is weaker than the strong open set condition and is not equivalent to the weak separation property. We show that the set of N-tuples of contractive homeomorphisms, which satisfy this separation condition is a G_delta set in the topology of pointwise convergence of every component mapping with an additional requirement that the supremum of contraction coefficients of mappings in the sequence be strictly less than one.We also give several sufficient conditions for this separation property. For every fixed N-tuple of dXd invertible contraction matrices from a certain class, we obtain density results for vectors of fixed points, which defineN-tuples of affine contraction mappings having this separation property. Joint work with Tim Bedford (University of Strathclyde) and Jeff Geronimo (Georgia Tech).

- Series
- Stochastics Seminar
- Time
- Thursday, November 12, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Gauri Data – University of Georgia

We consider two problems: (1) estimate a normal mean under a general
divergence loss introduced in Amari (1982) and Cressie and Read
(1984) and (2) find a predictive density of a new observation drawn
independently of the sampled observations from a normal distribution
with the same mean but possibly with a different variance under the
same loss. The general divergence loss includes as special cases
both the Kullback-Leibler and Bhattacharyya-Hellinger losses. The
sample mean, which is a Bayes estimator of the population mean under
this loss and the improper uniform prior, is shown to be minimax in
any arbitrary dimension. A counterpart of this result for predictive
density is also proved in any arbitrary dimension. The admissibility of
these rules
holds in one dimension, and we conjecture that the result is true in
two dimensions as well. However, the general Baranchik (1970) class
of estimators, which includes the James-Stein estimator and the
Strawderman (1971) class of estimators, dominates the sample mean in
three or higher dimensions for the estimation problem. An analogous
class of predictive densities is defined and any member of this
class is shown to dominate the predictive density corresponding to a
uniform prior in three or higher dimensions. For the prediction
problem, in the special case of Kullback-Leibler loss, our results
complement to a certain extent some of the recent important work of
Komaki (2001) and George, Liang and Xu (2006). While our proposed
approach produces a general class of predictive densities (not necessarily
Bayes) dominating the predictive density under a uniform prior,
George et al. (2006) produced a class of Bayes
predictors achieving a similar dominance. We show also that various
modifications of the James-Stein estimator continue to dominate the
sample mean, and by the duality of the estimation and predictive
density results which we will show, similar results continue to hold
for the prediction problem as well.
This is a joint research with Professor Malay Ghosh and Dr. Victor Mergel.

- Series
- ACO Colloquium
- Time
- Thursday, November 12, 2009 - 16:30 for 2 hours
- Location
- Skiles 255
- Speaker
- Miklos Simonovits – Alfred Renyi Institute, Budapest, Hungary

In my talk I will give a survey on the rise and early development of Extremal Graph Theory, one of the large areas in Discrete Mathematics.I will give a description of the asymptotic solution of extremal graph problems for ordinary graphs, describe the stability method and expose the difficulties connected to hypergraph extremal problems.I will expose several unsolved problems in the field, and move on to some new results.I will also describe the connection of the field to several other areas of Discrete Mathematics, like to Ramsey Theory,Random graphs, Regularity lemma, Quasi-randomness, etc.I will also mention some applications of extremal graph theory. The lecture will be a non-technical one.***Refreshments at 4PM in Skiles 236.***

- Series
- SIAM Student Seminar
- Time
- Friday, November 13, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Yao Li – School of Mathematics, Georgia Tech

Gibbs free energy plays an important role in thermodynamics and has strong connection with PDE, Dynamical system. The results about Gibbsfree energy in 2-Wasserstein metric space are known recently.First I will introduce some basic things, so the background knowledge isnot required. I will begin from the classic definition of Gibbs freeenergy functional and then move to the connection between Gibbs freeenergy and the Fokker-Planck equation, random perturbation of gradientsystems. Second, I will go reversely: from a dynamical system to thegeneralized Gibbs free energy functional. I will also talk about animportant property of the Gibbs free energy functional: TheFokker-Planck equation is the gradient flux of Gibbs free energyfunctional in 2-Wasserstein metric.So it is natural to consider a question: In topological dynamical systemand lattice dynamical system, could we give the similar definition ofGibbs free energy, Fokker-Planck equation and so on? If time allowed, Iwill basicly introduce some of my results in these topics.

- Series
- Combinatorics Seminar
- Time
- Friday, November 13, 2009 - 15:05 for 2 hours
- Location
- Skiles 255
- Speaker
- Miklos Simonovits – Alfred Renyi Institute, Budapest, Hungary

Stability methods are often used in extremal graph theory, Ramsey theory and similar areas, where an extremal problem is to be solved and

- we have a conjecture about the structure of the conjectured extremal configurations and according to our conjecture, it has some given property \mathcal P;
- we can prove that all the almost extremal structures are near to the property \mathcal P, in some sense;
- if we knew that if a structure is near to the property \mathcal P and is extremal, then it is already the conjectured structure.

Of course, stability methods can also be used in other cases, but we restrict ourselves to the above two areas.

In my lecture I will give an introduction to the applications of the stability methods in extremal graph theory, describe cases in extremal graph theory, extremal hypergraph theory, in the Erdos-Frankl-Rold (= generalized Erdos-Kleitman-Rothschild theory) ...

In the second part of my lecture I shall describe the application of this method to the Erdos-Sos conjecture. This is part of our work with Ajtai, Komlos and Szemeredi.

- Series
- CDSNS Colloquium
- Time
- Monday, November 16, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Wei-Min Wang – Universite Paris-Sud, France

We present a new theory on Hamiltonian PDE. The linear theory
solves an old spectral problem on boundedness of L infinity
norm of the eigenfunctions of the Schroedinger operator on the
2-torus. The nonlinear theory develops Fourier geometry, eliminates the convexity
condition on the (infinite dimension)
Hamiltonian and is natural for PDE.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, November 16, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Chris Rycroft – UC-Berkeley

Due to an incomplete picture of the underlying physics, the simulation
of dense granular flow remains a difficult computational challenge.
Currently, modeling in practical and industrial situations would
typically be carried out by using the Discrete-Element Method (DEM),
individually simulating particles according to Newton's Laws. The
contact models in these simulations are stiff and require very small
timesteps to integrate accurately, meaning that even relatively small
problems require days or weeks to run on a parallel computer. These
brute-force approaches often provide little insight into the relevant
collective physics, and they are infeasible for applications in
real-time process control, or in optimization, where there is a need to
run many different configurations much more rapidly.
Based upon a number of recent theoretical advances, a general
multiscale simulation technique for dense granular flow will be
presented, that couples a macroscopic continuum theory to a discrete
microscopic mechanism for particle motion. The technique can be applied
to arbitrary slow, dense granular flows, and can reproduce similar flow
fields and microscopic packing structure estimates as in DEM. Since
forces and stress are coarse-grained, the simulation technique runs two
to three orders of magnitude faster than conventional DEM. A particular
strength is the ability to capture particle diffusion, allowing for the
optimization of granular mixing, by running an ensemble of different
possible configurations.

- Series
- Analysis Working Seminar
- Time
- Monday, November 16, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Brett Wick – Georgia Tech

We are going to continue explaining the proof of Seip's Interpolation
Theorem for the Bergman Space. We are going to demonstrate the
sufficiency of these conditions for a certain example. We then will
show how to deduce the full theorem with appropriate modifications of
the example.

- Series
- PDE Seminar
- Time
- Tuesday, November 17, 2009 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Ning Jiang – Courant Institute, New York University

In a bounded domain with smooth boundary (which can be considered as a
smooth sub-manifold of R3), we consider the Boltzmann equation with
general Maxwell boundary condition---linear combination of specular
reflection and diffusive absorption. We analyze the kinetic (Knudsen
layer) and fluid (viscous layer) coupled boundary layers in both acoustic
and incompressible regimes, in which the boundary layers behave
significantly different. The existence and damping properties of these
kinetic-fluid layers depends on the relative size of accommodation number
and Kundsen number, and the differential geometric property of the
boundary (the second fundamental form.)
As applications, first we justify the incompressible Navier-Stokes-Fourier
limit of the Boltzmann equation with Dirichlet, Navier, and diffusive
boundary conditions respectively, depending on the relative size of
accommodation number and Kundsen number. Using the damping property of the
boundary layer in acoustic regime, we proved the convergence is strong.
The second application is that we derive and justified the higher order
acoustic approximation of the Boltzmann equation.
This is a joint work with Nader Masmoudi.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, November 18, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Jaap de Roode – Emory University

Host: Meghan Duffy (School of Biology, Georgia Tech)

Why do parasites cause disease? Theory has shown that natural selection could select for virulent parasites if virulence is correlated with between-host parasite transmission. Because ecological conditions may affect virulence and transmission, theory further predicts that adaptive levels of virulence depend on the specific environment in which hosts and parasites interact. To test these predictions in a natural system, we study monarch butterflies (Danaus plexippus) and their protozoan parasite (Ophryocystis elektroscirrha). Our studies have shown that more virulent parasites obtain greater between-host transmission, and that parasites with intermediate levels of virulence obtain highest fitness. The average virulence of wild parasite isolates falls closely to this optimum level, providing additional support that virulence can evolve as a consequence of natural selection operating on parasite transmission. Our studies have also shown that parasites from geographically separated populations differ in their virulence, suggesting that population-specific ecological factors shape adaptive levels of virulence. One important ecological factor is the monarch larval host plants in the milkweed family. Monarch populations differ in the milkweed species they harbor, and experiments have shown that milkweeds can alter parasite virulence. Our running hypothesis is that plant availability shapes adaptive levels of parasite virulence in natural monarch populations. Testing this hypothesis will improve our understanding of why some parasites are more harmful than others, and will help with predicting the consequences of human actions on the evolution of disease.

- Series
- Research Horizons Seminar
- Time
- Wednesday, November 18, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Drs. Ulmer, Harrell, and Wick – School of Mathematics, Georgia Tech

The Research Horizons seminar this week will be a panel discussion on
the academic job market for mathematicians. The discussion will begin
with an overview by Doug Ulmer of the hiring process, with a focus on
the case of research-oriented universities. The panel will then take
questions from the audience. Professor Wick was hired last year at
Tech, so has recently been on the students' side of the process.
Professor Harrell has been involved with hiring at Tech for many years
and can provide a perspective on the university side of the process.

- Series
- Other Talks
- Time
- Wednesday, November 18, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Doug Ulmer – Ga Tech

In the 60s, Grothendieck had the remarkable idea of introducing a new kind of topology where open coverings of X are no longer collections of subsets of X, but rather certain maps from other spaces to X. I will give some examples to show why this is reasonable and what one can do with it.

- Series
- Analysis Seminar
- Time
- Wednesday, November 18, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Matt Bond – Michigan State University

It is well known that a needle thrown at random has zero
probability of intersecting any given irregular planar set of finite
1-dimensional Hausdorff measure. Sharp quantitative estimates for fine open
coverings of such sets are still not known, even for such sets as the
Sierpinski gasket and the 4-corner Cantor set (with self-similarities 1/4
and 1/3). In 2008, Nazarov, Peres, and Volberg provided the sharpest known
upper bound for the 4-corner Cantor set. Volberg and I have recently used
the same ideas to get a similar estimate for the Sierpinski gasket. Namely,
the probability that Buffon's needle will land in a 3^{-n}-neighborhood of
the Sierpinski gasket is no more than C_p/n^p, where p is any small enough
positive number.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, November 19, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Christine Heitsch – School of Mathematics, Georgia Tech

Understanding the folding of RNA sequences into three-dimensional structures is one of the fundamental challenges in molecular biology. In this talk, we focus on understanding how an RNA viral genome can fold into the dodecahedral cage known from experimental data. Using strings and trees as a combinatorial model of RNA folding, we give mathematical results which yield insight into RNA structure formation and suggest new directions in viral capsid assembly. We also illustrate how the interaction between discrete mathematics and molecular biology motivates new combinatorial theorems as well as advancing biomedical applications.

- Series
- Graph Theory Seminar
- Time
- Thursday, November 19, 2009 - 12:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Graham Brightwell – London School of Economics

Several interesting models of random partial orders can be described via a
process that builds the partial order one step at a time, at each point
adding a new maximal element. This process therefore generates a linear
extension of the partial order in tandem with the partial order itself. A
natural condition to demand of such processes is that, if we condition on
the occurrence of some finite partial order after a given number of steps,
then each linear extension of that partial order is equally likely. This
condition is called "order-invariance".
The class of order-invariant processes includes processes generating a
random infinite partial order, as well as those that amount to taking a
random linear extension of a fixed infinite poset.
Our goal is to study order-invariant processes in general. In this talk, I
shall focus on some of the combinatorial problems that arise.
(joint work with Malwina Luczak)

- Series
- PDE Seminar
- Time
- Thursday, November 19, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Zhouping Xin – The Chinese University of Hong Kong

One of the challenges in the study of transonic flows is the understanding of
the flow behavior near the sonic state due to the severe degeneracy of the
governing equations. In this talk, I will discuss the well-posedness theory of a
degenerate free boundary problem for a quasilinear second elliptic equation
arising from studying steady subsonic-sonic irrotational compressible flows in a convergent nozzle. The flow speed is sonic at the free boundary where the potential flow equation becomes degenerate. Both existence and uniqueness will be shown and optimal regularity will be obtained. Smooth transonic flows in deLaval nozzles
will also be discussed. This is a joint work with Chunpeng Wang.

- Series
- Stochastics Seminar
- Time
- Thursday, November 19, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Lijian Yang – Michigan State University

Recently functional data analysis has received considerable attention in
statistics research and a number of successful applications have been reported, but
there has been no results on the inference of the global shape of the mean regression
curve. In this paper, asymptotically simultaneous confidence band is obtained for the
mean trajectory curve based on sparse longitudinal data, using piecewise constant
spline estimation. Simulation experiments corroborate the asymptotic theory.

- Series
- SIAM Student Seminar
- Time
- Friday, November 20, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Huy Huynh – Georgia Tech

Let X_1, X_2,...,X_n be a sequence of i.i.d random variables with
values in a finite alphabet {1,...,m}. Let LI_n be the length of the
longest increasing subsequence of X_1,...,X_n. We shall express the
limiting distribution of LI_n as functionals of m and (m-1)-
dimensional Brownian motions as well as the largest eigenvalue of
Gaussian Unitary Ensemble (GUE) matrix. Then I shall illustrate
simulation study of these results

- Series
- Combinatorics Seminar
- Time
- Friday, November 20, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 255
- Speaker
- Mark Ellingham – Vanderbilt University

Linkage involves finding a set of internally disjoint paths in a graph with specified endpoints. Given graphs G and H, we say G is H-linked if for every injective mapping f:V(H) -> V(G) we can find a subgraph H' of G which is a subdivision of H, with f(v) being the vertex of H' corresponding to each vertex v of H. We describe two results on H-linkage for small graphs H.

(1) Goddard showed that 4-connected planar triangulations are 4-ordered, or in other words C_4-linked. We strengthen this by showing that 4-connected planar triangulations are (K_4-e)-linked.

(2) Xingxing Yu characterized certain graphs related to P_4-linkage. We use his characterization to show that every 7-connected graph is P_4-linked, and to construct 6-connected graphs that are not P_4-linked.

This is joint work with Michael D. Plummer and Gexin Yu.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, November 23, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Xiaoming Huo – Georgia Tech (School of ISyE) – xiaoming@isye.gatech.edu

Many algorithms were proposed in the past ten years on utilizing manifold structure for dimension reduction. Interestingly, many algorithms ended up with computing for eigen-subspaces. Applying theorems from matrix perturbation, we study the consistency and rate of convergence of some manifold-based learning algorithm. In particular, we studied local tangent space alignment (Zhang & Zha 2004) and give a worst-case upper bound on its performance. Some conjectures on the rate of convergence are made. It's a joint work with a former student, Andrew Smith.

- Series
- Geometry Topology Seminar
- Time
- Monday, November 23, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Hong-Van Le – Mathematical Institute of Academy of Sciences of the Czech Republic

In 1979 Valiant gave algebraic analogs to algorithmic complexity problem such as $P \not = NP$. His central conjecture concerns the determinantal complexity of the permanents. In my lecture I shall propose geometric and algebraic methods to attack this problem and other lower bound problems based on the elusive functions approach by Raz. In particular I shall give new algorithms to get lower bounds for determinantal complexity of polynomials over $Q$, $R$ and $C$.

- Series
- Algebra Seminar
- Time
- Monday, November 23, 2009 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Anton Leykin – Georgia Tech

This talk will start with an introduction to the area of numerical algebraic geometry. The homotopy continuation algorithms that it currently utilizes are based on heuristics: in general their results are not certified. Jointly with Carlos Beltran, using recent developments in theoretical complexity analysis of numerical computation, we have implemented a practical homotopy tracking algorithm that provides the status of a mathematical proof to its approximate numerical output.

- Series
- Other Talks
- Time
- Wednesday, November 25, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Matt Baker – School of Mathematics, Georgia Tech

We will state Serre's fundamental finiteness and vanishing results for the cohomology
of coherent sheaves on a projective algebraic variety. As an application, we'll prove that the
constant term of the Hilbert Polynomial does not depend on the projective embedding, a fact which
is hard to understand using classical (non-cohomological) methods.

- Series
- CDSNS Colloquium
- Time
- Monday, November 30, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Maria Lopez – Consejo Superior de Investigaciones Cientificas Madrid, Spain

We introduce a change of coordinates allowing to capture in a fixed reference frame the profile of travelling wave solutions for nonlinear parabolic equations. For nonlinearities of bistable type the asymptotic travelling wave profile becomes an equilibrium state for the augmented reaction-diffusion equation. In the new equation, the profile of the asymptotic travelling front and its propagation speed emerge simultaneously as time evolves. Several numerical experiments illustrate the effciency of the method.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, November 30, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- David Hu – Georgia Tech ME

How do animals move without legs? In this experimental and theoretical
study, we investigate the slithering of snakes on flat surfaces.
Previous studies of slithering have rested on the assumption that
snakes slither by pushing laterally against rocks and branches. In this
combined experimental and theoretical study, we develop a model for
slithering locomotion by observing snake motion kinematics and
experimentally measuring the friction coefficients of snake skin. Our
predictions of body speed show good agreement with observations,
demonstrating that snake propulsion on flat ground, and possibly in
general, relies critically on the frictional anisotropy of their
scales. We also highlight the importance of the snake's dynamically
redistributing its weight during locomotion in order to improve speed
and efficiency. We conclude with an overview of our experimental
observations of other methods of propulsion by snakes, including
sidewinding and a unidirectional accordion-like mode.

- Series
- Analysis Working Seminar
- Time
- Monday, November 30, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Brett Wick – Georgia Tech

We are going to finish explaining the proof of Seip's Interpolation
Theorem for the Bergman Space. This will be the last meeting of the seminar for the semester.

- Series
- Geometry Topology Seminar
- Time
- Monday, November 30, 2009 - 14:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Stavros Garoufalidis – Georgia Tech – stavros@math.gatech.edu

I will discuss a conjecture that relates the degree of the Jones polynomial of a knot and its parallels with the slopes of incompressible surfaces in the knot complement. I will present examples, as well as computational challenges.

- Series
- PDE Seminar
- Time
- Tuesday, December 1, 2009 - 15:01 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Jose Arrieta – Universidad Complutense de Madrid; visiting faculty at GT

In this talk we will present several results concerning the behavior of the Laplace operator with Neumann boundary conditions in a thin domain where its boundary presents a highly oscillatory behavior. Using homogenization and domain perturbation techniques, we obtain the asymptotic limit as the thickness of the domain goes to zero even for the case where the oscillations are not necessarily periodic. We will also indicate how this result can be applied to analyze the asymptotic dynamics of reaction diffusion equations in these domains.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, December 2, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Laura Miller – University of North Carolina at Chapel Hill

The Reynolds number (Re) is often used to describe scaling effects in ﬂuid dynamics and may be thought of as roughly describing the ratio of inertial to viscous forces in the ﬂuid. It can be shown that ’reciprocal’ methods of macroscopic propulsion (e.g. ﬂapping, undulating, and jetting) do not work in the limit as Re approaches zero. However, such macroscopic forms of locomotion do not appear in nature below Re on the order of 1 − 10. Similarly, macroscopic forms of feeding do not occur below a similar range of Reynolds numbers. The focus of this presentation is to describe the scaling effects in feeding and swimming of the upside down jellyﬁsh (Cassiopeia sp.) using computational fluid dynamics and experiments with live animals. The immersed boundary method is used to solve the Navier-Stokes equations with an immersed, flexible boundary. Particle image velocimetry is used to quantify the flow field around the live jellyfish and compare it to the simulations.

- Series
- Research Horizons Seminar
- Time
- Wednesday, December 2, 2009 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 171
- Speaker
- John McCuan – School of Mathematics, Georgia Tech – mccuan@math.gatech.edu

I will describe several geometrical problems that arise from
the minimization of some sort of integral functional and the basic
relation between such minimization and partial differential equations.
Then I will make some further comments on my favorite kind of such
problems, namely those that have something to do with minimizing area of
surfaces under various side conditions.

- Series
- Other Talks
- Time
- Wednesday, December 2, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Kangkang Wang – School of Mathematics, Georgia Tech

We will present a sheaf-theoretic proof of the Riemann-Roch theorem
for projective nonsingular curves.

- Series
- Analysis Seminar
- Time
- Wednesday, December 2, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Alexander Stokolos – Georgia Southern University

I will speak about an extension of Cordoba-Feﬀerman Theorem on the equivalence between boundedness properties of certain classes of maximal and multiplier operators. This extension utilizes the recent work of Mike Bateman on directional maximal operators as well as my work with Paul Hagelstein on geometric maximal operators associated to homothecy invariant bases of convex sets satisfying Tauberian conditions.

- Series
- Graph Theory Seminar
- Time
- Thursday, December 3, 2009 - 12:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Carl Yerger – Math, GT

A fundamental question in topological graph theory is as follows: Given a surface S and an integer t > 0, which graphs drawn in S are t-colorable? We say that a graph is (t+1)-critical if it is not t-colorable, but every proper subgraph is. In 1993, Carsten Thomassen showed that there are only finitely many six-critical graphs on a fixed surface with Euler genus g. In this talk, I will describe a new short proof of this fact. In addition, I will describe some structural lemmas that were useful to the proof and describe a list-coloring extension that is helpful to ongoing work that there are finitely many six-list-critical graphs on a fixed surface. This is a joint project with Ken-ichi Kawarabayashi of the National Institute of Informatics, Tokyo.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, December 4, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Jim Krysiak – School of Mathematics, Georgia Tech

This talk will mostly be exposition on a result of M. Ghomi that
any C^2 knot in R^n can be C^1 perturbed into a knot of constant curvature
while preserving any smoothness properties.

- Series
- Other Talks
- Time
- Friday, December 4, 2009 - 15:00 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 168
- Speaker
- Michelle Delcourt and Leo Chen – School of Mathematics, Georgia Tech

Leo Chen: The Shape and Stability of a Flexible Sheet in a von Karman Vortex Street

Michelle Delcourt: Dessin and Manturov bracket shuffles

In this talk we will explore the connections between knot theory and combinatorics. Links are related to Grothendieck's dessins d'enfants. Cartographic one-vertex dessins can be represented by chord diagrams. The diagrams can be recorded as "words" using a finite alphabet (k-bracket parenthesis system). Many combinatorial objects are related to these Manturov bracket structures.

- Series
- Other Talks
- Time
- Monday, December 7, 2009 - 08:00 for 8 hours (full day)
- Location
- University of Alabama, Birmingham
- Speaker
- Southeast Geometry Seminar – University of Alabama, Birmingham

The Southeast Geometry Seminar is a series of semiannual one-day events focusing on geometric analysis. These events are hosted in rotation by the following institutions:

- The University of Alabama at Birmingham
- The Georgia Institute of Technology
- Emory University
- The University of Tennessee Knoxville

The following five speakers will give presentations on topics that include geometric analysis, and related fields, such as partial differential equations, general relativity, and geometric topology.

- Natasa Sesum (U Penn)
- Alexandru Ionescu (U Wisconsin)
- Sergiu Klainerman (Princeton U)
- Alex Freire (U Tennessee Knoxville)
- Christian Hainzl (UAB)

A poster session will be hosted. There will also be an evening public lecture by plenary speaker Sergiu Klainerman entitled The Mathematical Magic of Black Holes.

- Series
- Job Candidate Talk
- Time
- Monday, December 7, 2009 - 14:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Robert Young – IHES/Courant

The Dehn function is a group invariant which connects geometric and combinatorial group theory; it measures both the difficulty of the word problem and the area necessary to fill a closed curve in an associated space with a disc. The behavior of the Dehn function for high-rank lattices in high-rank symmetric spaces has long been an openquestion; one particularly interesting case is SL(n,Z). Thurston conjectured that SL(n,Z) has a quadratic Dehn function when n>=4. This differs from the behavior for n=2 (when the Dehn function is linear) and for n=3 (when it is exponential). I have proved Thurston's conjecture when n>=5, and in this talk, I will give an introduction to the Dehn function, discuss some of the background of the problem and, time permitting, give a sketch of the proof.

- Series
- Job Candidate Talk
- Time
- Tuesday, December 8, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Xia Hua – Massachusetts Institute of Technology

In a regression model, say Y_i=f(X_i)+\epsilon_i, where (X_i,Y_i) are observed and f is an unknown regression function, the errors \epsilon_i may satisfy what we call the "weak'' assumption that they are orthogonal with mean 0 and the same variance, and often the further ``strong'' assumption that they are i.i.d. N(0,\sigma^2) for some \sigma\geq 0. In this talk, I will focus on the polynomial regression model, namely f(x) = \sum_{i=0}^n a_i x^i for unknown parameters a_i, under the strong assumption on the errors. When a_i's are estimated via least squares (equivalent to maximum likelihood) by \hat a_i, we then get the {\it residuals} \hat epsilon_j := Y_j-\sum_{i=0}^n\hat a_iX_j^i. We would like to test the hypothesis that the nth order polynomial regression holds with \epsilon_j i.i.d. N(0,\sigma^2) while the alternative can simply be the negation or be more specific, e.g., polynomial regression with order higher than n. I will talk about two possible tests, first the rather well known turning point test, and second a possibly new "convexity point test.'' Here the errors \epsilon_j are unobserved but for large enough n, if the model holds, \hat a_i will be close enough to the true a_i so that \hat epsilon_j will have approximately the properties of \epsilon_j. The turning point test would be applicable either by this approximation or in case one can evaluate the distribution of the turning point statistic for residuals. The "convexity point test'' for which the test statistic is actually the same whether applied to the errors \epsilon_j or the residuals \hat epsilon_j avoids the approximation required in applying the turning point test to residuals. On the other hand the null distribution of the convexity point statistic depends on the assumption of i.i.d. normal (not only continuously distributed) errors.

- Series
- Mathematical Finance/Financial Engineering Seminar
- Time
- Tuesday, December 8, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Peter Laurence – Courant Institute of Mathematical Science, New York University

We focus on time inhomogeneous local volatility models, the cornerstone of projection methods of higher dimensional models, and show how to use the heat kernel expansion to obtain new and, in some sense optimal, expansions of the implied volatility in the time to maturity variable. This is joint work with Jim Gatheral, Elton Hsu, Cheng Ouyang and Tai-Ho Wang.

- Series
- Analysis Seminar
- Time
- Tuesday, December 8, 2009 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Xuan Duong – Macquarie University

In this talk,we study weighted L^p-norm inequalities for general spectralmultipliersfor self-adjoint positive definite operators on L^2(X), where X is a space of homogeneous type. We show that the sharp weighted Hormander-type spectral multiplier theorems follow from the appropriate estimatesof the L^2 norm of the kernel of spectral multipliers and the Gaussian boundsfor the corresponding heat kernels. These results are applicable to spectral multipliersfor group invariant Laplace operators acting on Lie groups of polynomialgrowth and elliptic operators on compact manifolds. This is joint work with Adam Sikora and Lixin Yan.

- Series
- Job Candidate Talk
- Time
- Thursday, January 7, 2010 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Dan Margalit – Tufts University – Dan.Margalit@tufts.edu

Attached to every homeomorphism of a surface is a real number called its dilatation. For a generic (i.e. pseudo-Anosov) homeomorphism, the dilatation is an algebraic integer that records various properties of the map. For instance, it determines the entropy (dynamics), the growth rate of lengths of geodesics under iteration (geometry), the growth rate of intersection numbers under iteration (topology), and the length of the corresponding loop in moduli space (complex analysis). The set of possible dilatations is quite mysterious. In this talk I will explain the discovery, joint with Benson Farb and Chris Leininger, of two universality phenomena. The first can be described as "algebraic complexity implies dynamical complexity", and the second as "geometric complexity implies dynamical complexity".

- Series
- Geometry Topology Seminar
- Time
- Sunday, January 10, 2010 - 15:00 for 1 hour (actually 50 minutes)
- Location
- TBA
- Speaker
- Matt Clay – Allegheny College

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, January 11, 2010 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Peter Blomgren – San Diego State University

We describe two computational frameworks for the assessment of contractileresponses of enzymatically dissociated adult and neonatal cardiac myocytes.The proposed methodologies are variants of mathematically sound andcomputationally robust algorithms very well established in the imageprocessing community. The physiologic applications of the methodologies areevaluated by assessing the contraction in enzymatically dissociated adultand neonatal rat cardiocytes. Our results demonstrate the effectiveness ofthe proposed approaches in characterizing the true 'shortening' in thecontraction process of the cardiocytes. The proposed method not onlyprovides a more comprehensive assessment of the myocyte contraction process,but can potentially eliminate historical concerns and sources of errorscaused by myocyte rotation or translation during contraction. Furthermore,the versatility of the image processing techniques makes the methodssuitable for determining myocyte shortening in cells that usually bend ormove during contraction. The proposed method can be utilized to evaluatechanges in contractile behavior resulting from drug intervention, diseasemodeling, transgeneity, or other common applications to mammaliancardiocytes.This is research is in collaboration with Carlos Bazan, David Torres, andPaul Paolini.

- Series
- Analysis Seminar
- Time
- Wednesday, January 13, 2010 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Gerald Beer – California State University, Los Angeles

Sandro Levi and I have investigated variational strengthenings of uniform continuity and uniform convergence of nets or sequences of functions with respect to a family of subsets of the domain. Out of our theory comes an answer to this basic question: what is the weakest topology stronger than the topology of pointwise convergence in which continuity is preserved under taking limits? We argue that the classical theory constitues a misunderstanding of what is fundamentally a variational phenomenon.

- Series
- ACO Colloquium
- Time
- Thursday, January 14, 2010 - 16:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Amin Saberi – Stanford University

Refreshments at 4:00PM in Skiles 236

I will talk about new approximation algorithms for the Asymmetric Traveling Salesman Problem (ATSP) when the costs satisfy the triangle inequality. Our approach is based on constructing a "thin" spanning tree from the solution of a classical linear programming relaxation of the problem and augmenting the tree to an Eulerian subgraph. I will talk about Goddyn's conjecture on the existence of such trees and its relations to nowhere-zero flows. I will present an O(log n/log log n) approximation algorithm that uses a new randomized rounding method. Our rounding method is based on sampling from a distribution and could be of independent interest. Also, I will talk about the special case where the underlying undirected graph of the LP relaxation of the problem has bounded genus. This is the case for example, when the distance functions are shortest paths in a city with few bridges and underpasses. We give a constant factor approximation algorithm in that case. The first result is a joint work with A. Asadpour, M. Goemans, A. Madry and S. Oveis Gharan, and the second result is a joint work with S. Oveis Gharan.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, January 15, 2010 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Mohammad Ghomi – Georgia Tech

We study the topology of the space bd K^n of complete convex
hypersurfaces of R^n which are homeomorphic to R^{n-1}. In particular,
using Minkowski sums, we construct a deformation retraction of bd K^n
onto the Grassmannian space of hyperplanes. So every hypersurface in bd
K^n may be flattened in a canonical way. Further, the total curvature
of each hypersurface evolves continuously and monotonically under this
deformation. We also show that, modulo proper rotations, the subspaces
of bd K^n consisting of smooth, strictly convex, or positively curved
hypersurfaces are each contractible, which settles a question of H.
Rosenberg.

- Series
- Job Candidate Talk
- Time
- Tuesday, January 19, 2010 - 11:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Pavlo Pylyavskyy – University of Michigan

The Edrei-Thoma theorem characterizes totally positive functions, and plays an important role in character theory of the infinite symmetric group. The Loewner-Whitney theorem characterizes totally positive elements of the general linear group, and is fundamental for Lusztig's theory of total positivity in reductive groups. In this work we derive a common generalization of the two theorems. The talk is based on joint work with Thomas Lam.

- Series
- PDE Seminar
- Time
- Tuesday, January 19, 2010 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Michael I. Weinstein – Columbia University

I will discuss the intermediate and long time dynamics
of solutions of the nonlinear Schroedinger - Gross Pitaevskii equation,
governing nonlinear dispersive waves in a spatially
non-homogeneous background.
In particular, we present results (with B. Ilan)
on solitons with frequencies near a spectral band edge associated
with periodic potential, and results (with Z. Gang) on large
time energy distribution in systems with multiple bound states.
Finally, we discuss how such results can inform strategies
for control of soliton-like states in optical and quantum systems.

- Series
- Algebra Seminar
- Time
- Tuesday, January 19, 2010 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Clay Petsche – Hunter College

Weyl proved that if an N-dimensional real vector v has linearly independent coordinates over Q, then its integer multiples v, 2v, 3v, .... are uniformly distributed modulo 1. Stated multiplicatively (via the exponential map), this can be viewed as a Haar-equidistribution result for the cyclic group generated by a point on the N-dimensional complex unit torus. I will discuss an analogue of this result over a non-Archimedean field K, in which the equidistribution takes place on the N-dimensional Berkovich projective space over K. The proof uses a general criterion for non-Archimedean equidistribution, along with a theorem of Mordell-Lang type for the group variety G_m^N over the residue field of K, which is due to Laurent.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, January 20, 2010 - 11:00 for 1 hour (actually 50 minutes)
- Location
- SKiles 269
- Speaker
- Lee Childers – Georgia Tech, School of Applied Physiology – lee@gatech.edu

Cycling represents an integration of man and machine. Optimizing this integration through changes in rider position or bicycle component selection may enhance performance of the total bicycle/rider system. Increasing bicycle/rider performance via mathematical modeling was accomplished during the US Olympic Superbike program in preparation for the 1996 Atlanta Olympic Games. The purpose of this presentation is to provide an overview on the science of cycling with an emphasis on biomechanics using the track pursuit as an example. The presentation will discuss integration and interaction between the bicycle and human physiological systems, how performance may be measured in a laboratory as well as factors affecting performance with an emphasis on biomechanics. Then reviewing how people pedal a bicycle with attention focused on forces at the pedal and the effect of position variables on performance. Concluding with how scientists working on the US Olympic Superbike program incorporated biomechanics and aerodynamic test data into a mathematical model to optimize team pursuit performance during the 1996 Atlanta Olympic Games.

- Series
- Analysis Seminar
- Time
- Wednesday, January 20, 2010 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Úlfar Stefánsson – Georgia Tech

Müntz polynomials arise from consideration of Müntz's Theorem, which is a beautiful generalization of Weierstrass's Theorem. We prove a new surprisingly simple representation for the Müntz orthogonal polynomials on the interval of orthogonality, and in particular obtain new formulas for some of the classical orthogonal polynomials (e.g. Legendre, Jacobi, Laguerre). This allows us to determine the strong asymptotics on the interval, and the zero spacing behavior follows. This is the first time that such asymptotics have been obtained for general Müntz exponents. We also look at the asymptotic behavior outside the interval, and the asymptotic properties of the associated Christoffel functions.

- Series
- Joint School of Mathematics and ACO Colloquium
- Time
- Thursday, January 21, 2010 - 11:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Bruce Reed – McGill University

The term Probabilistic Method refers to the proof of
deterministic statements using probabilistic tools. Two of the most famous
examples arise in number theory. these are: the first non-analytic proof
of the prime number theorem given by Erdos in the 1940s, and the recent
proof of the Hardy-Littlewood Conjecture (that there are arbitrarily long
arithmetic progressions of primes) by Green and Tao.
The method has also been succesfully applied in the field of graph
colouring. We survey some of the results thereby obtained.
The talk is targeted at a general audience. We will first define graph
colouring, explain the type of graph colouring problems which tend to
attract interest, and then explain the probabilistic tools which are
used
to solve them, and why we would expect the type of tools that are used to
be effective for solving the types of problems typically studied.

- Series
- Job Candidate Talk
- Time
- Thursday, January 21, 2010 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Yekaterina Epshteyn – Carnegie Mellon University

In this talk, I will first discuss several chemotaxis models includingthe classical Keller-Segel model.Chemotaxis is the phenomenon in which cells, bacteria, and other single-cell or multicellular organisms direct their movements according to certain chemicals (chemoattractants) in their environment. The mathematical models of chemotaxis are usually described by highly nonlinear time dependent systems of PDEs. Therefore, accurate and efficient numerical methods are very important for the validation and analysis of these systems. Furthermore, a common property of all existing chemotaxis systems is their ability to model a concentration phenomenon that mathematically results in solutions rapidly growing in small neighborhoods of concentration points/curves. The solutions may blow up or may exhibit a very singular, spiky behavior. In either case, capturing such solutions numerically is a challenging problem. In our work we propose a family of stable (even at times near blow up) and highly accurate numerical methods, based on interior penalty discontinuous Galerkin schemes (IPDG) for the Keller-Segel chemotaxis model with parabolic-parabolic coupling. This model is the basic step in the modeling of many real biological processes and it is described by a system of a convection-diffusion equation for the cell density, coupled with a reaction-diffusion equation for the chemoattractant concentration.We prove theoretical hp error estimates for the proposed discontinuous Galerkin schemes. Our proof is valid for pre-blow-up times since we assume boundedness of the exact solution.Numerical experiments to demonstrate the stability and accuracy of the proposed methods for chemotaxis models and comparison with other methods will be presented. Ongoing research projects will be discussed as well.

- Series
- SIAM Student Seminar
- Time
- Friday, January 22, 2010 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Benjamin Webb – School of Mathematics, Georgia Tech

The Fundamental Theorem of Algebra implies that a complex valued nxn matrix has n eigenvalues (including multiplicities). In this talk we introduce a general method for reducing the size of a square matrix while preserving this spectrum. This can then be used to improve on the classic eigenvalue estimates of Gershgorin, Brauer, and Brualdi. As this process has a natural graph theoretic interpretation this talk should be accessible to most anyone with a basic understanding of matrices and graphs. These results are based on joint work with Dr. Bunimovich.

- Series
- Combinatorics Seminar
- Time
- Friday, January 22, 2010 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Keni-chi Kawarabayashi – National Institute of Informatics

Hajos' conjecture is false, and it seems that graphs without a
subdivision of a big complete graph do not behave as well as
those without a minor of a big complete graph.
In fact, the graph minor theorem (a proof of Wagner's
conjecture) is not true if we replace the minor relation by the
subdivision relation. I.e, For every infinite sequence
G_1,G_2, ... of graphs, there exist distinct integers
i < j such that G_i is a minor of G_j, but if we replace
''minor" by ''subdivision", this is no longer true.
This is partially because we do not really know what the graphs
without a subdivision of a big complete graph look like.
In this talk, we shall discuss this issue. In particular,
assuming some moderate connectivity condition, we can say
something, which we will present in this talk.
Topics also include coloring graphs without a subdivision of a
large complete graph, and some algorithmic aspects. Some of the
results are joint work with Theo Muller.

- Series
- Analysis Working Seminar
- Time
- Monday, January 25, 2010 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- James Curry – Ga Tech

This is the first meeting of a weekly working seminar on two weight inequalities in Harmonic Analysis. James Curry will present the paper arXiv:0911.3437, which proves two-weight norm inequalities for a class of dyadic, positive operators.

- Series
- Graph Theory Seminar
- Time
- Tuesday, January 26, 2010 - 10:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Sergey Norin – Princeton University

A graph G contains a graph H as a minor if a graph isomorphic to H can be obtained from a subgraph of G bycontracting edges. One of the central results of the rich theory of graph minors developed by Robertson and Seymour is an approximate description of graphs that do not contain a fixed graph as a minor. An exact description is only known in a few cases when the excluded minor is quite small.In recent joint work with Robin Thomas we have proved a conjecture of his, giving an exact characterization of all large, t-connected graphs G that do not contain K_t, the complete graph on t vertices, as a minor. Namely, we have shown that for every integer t there exists an integer N=N(t) such that a t-connected graph G on at least N vertices has no K_t minor if and only if G contains a set of at most t- 5 vertices whose deletion makes G planar. In this talk I will describe the motivation behind this result, outline its proof and mention potential applications of our methods to other problems.

- Series
- Job Candidate Talk
- Time
- Tuesday, January 26, 2010 - 11:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Shamgar Gurevich – Institute for Advanced Study, Princeton – shamgar@ias.edu

In the lecture I will explain how various fundamental structures from group representation theory appear naturally in the context of discrete harmonic analysis and can be applied to solve concrete problems from digital signal processing. I will begin the lecture by describing our solution to the problem of finding a canonical orthonormal basis of eigenfunctions of the discrete Fourier transform (DFT). Then I will explain how to generalize the construction to obtain a larger collection of functions that we call "The oscillator dictionary". Functions in the oscillator dictionary admit many interesting pseudo-random properties, in particular, I will explain several of these properties which arise in the context of problems of current interest in communication theory.

- Series
- Research Horizons Seminar
- Time
- Tuesday, January 26, 2010 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- John McCuan – School of Math, Georgia Tech

Hosted by: Huy Huynh and Yao Li

In the preceeding talk, I outlined a framework for variational problems
and some of the basic tools and results. In this talk I will attempt
describe several problems of current interest.

- Series
- PDE Seminar
- Time
- Tuesday, January 26, 2010 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Margaret Beck – Boston University

The large-time behavior of solutions to Burgers equation with small viscosity isdescribed using invariant manifolds. In particular, a geometric explanation is provided for aphenomenon known as metastability, which in the present context means that solutions spend avery long time near the family of solutions known as diffusive N-waves before finallyconverging to a stable self-similar diffusion wave. More precisely, it is shown that in termsof similarity, or scaling, variables in an algebraically weighted L^2 space, theself-similar diffusion waves correspond to a one-dimensional global center manifold ofstationary solutions. Through each of these fixed points there exists a one-dimensional,global, attractive, invariant manifold corresponding to the diffusive N-waves. Thus,metastability corresponds to a fast transient in which solutions approach this ``metastable"manifold of diffusive N-waves, followed by a slow decay along this manifold, and, finally,convergence to the self-similar diffusion wave. This is joint work with C. Eugene Wayne.

- Series
- Algebra Seminar
- Time
- Wednesday, January 27, 2010 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Shamgar Gurevich – Institute for Advanced Study, Princeton – shamgar@ias.edu

This is a sequel to my first talk on "group representation patterns in digital signal processing". It will be slightly more specialized. The finite Weil representation is the algebra object that governs the symmetries of Fourier analysis of the Hilbert space L^2(F_q). The main objective of my talk is to introduce the geometric Weil representation---developed in a joint work with Ronny Hadani---which is an algebra-geometric (l-adic perverse Weil sheaf) counterpart of the finite Weil representation. Then, I will explain how the geometric Weil representation is used to prove the main results stated in my first talk. In the course, I will explain the Grothendieck geometrization procedure by which sets are replaced by algebraic varieties and functions by sheaf theoretic objects.

- Series
- Other Talks
- Time
- Thursday, January 28, 2010 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 249
- Speaker
- Provost Gary Schuster – President&#039;s Office, Georgia Tech

- Series
- Analysis Seminar
- Time
- Thursday, January 28, 2010 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Mishko Mitkovski – Texas A&amp;M

Given a set of complex exponential e^{i \lambda_n x} how large do you have to take r so that the sequence is independent in L^2[-r,r] ? The answer is given in terms of the Beurling-Mallivan density.

- Series
- Stochastics Seminar
- Time
- Thursday, January 28, 2010 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Stefan Boettcher – Emory Physics

Finding ground states of spin glasses, a model of disordered materials,
has a deep connection to many hard combinatorial optimization problems,
such as satisfiability, maxcut, graph-bipartitioning, and coloring.
Much insight has been gained for the combinatorial problems from the
intuitive approaches developed in physics (such as replica theory and
the cavity method), some of which have been proven rigorously recently.
I present a treasure trove of numerical data obtained with heuristic
methods that suggest a number conjectures, such as an equivalence
between maxcut and bipartitioning for r-regular graphs, a simple
relation for their optimal configurations as a function of degree r,
and anomalous extreme-value fluctuations in a variety of models, hotly
debated in physics currently. For some, such as those related to
finite-size effects, not even a physics theory exists, for others
theory exists that calls for rigorous methods.

- Series
- Job Candidate Talk
- Time
- Thursday, January 28, 2010 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Josephine Yu – Georgia Tech

Tropical geometry can be thought of as geometry over the tropical
semiring, which is the set of real numbers together with the operations max
and +. Just as ordinary linear and polynomial algebra give rise to
convex geometry and algebraic geometry, tropical linear and polynomial
algebra give rise to tropical convex geometry and tropical algebraic
geometry. I will introduce the basic objects and problems in tropical
geometry and discuss some relations with, and applications to,
polyhedral geometry, computational algebra, and algebraic geometry.

- Series
- SIAM Student Seminar
- Time
- Friday, January 29, 2010 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Kai Ni – School of Mathematics, Georgia Tech

In 2006, my coadvisor Xiaoming Huo and his colleague published an
annal of statistics paper which designs an asymptotically powerful
testing algorithm to detect the potential curvilinear structure in a
messy point cloud image. However, such an algorithm involves a
membership threshold and a decision threshold which are not well
defined in that paper because the distribution of LSP was unknown.
Later on, Xiaoming's student Chen, Jihong found some connections
between the distribution of LSP and the so-called Erdos-Renyi law.
In some sense, the distribution of LSP is just a generalization of
the Erdos-Renyi law. However this JASA paper of Chen, Jihong had
some restrictions and only partially found out the distribution of
LSP. In this talk, I will show the result of the JASA paper is
actually very close to the distribution of LSP. However, these is
still much potential work to do in order to strengthen this
algorithm.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, January 29, 2010 - 14:00 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 269
- Speaker
- Mohammad Ghomi – School of Mathematics, Georgia Tech

We prove that convex hypersurfaces M in R^n which are level sets of functions f: R^n --> R are C^1-regular if f has a nonzero partial derivative of some order at each point of M. Furthermore, applying this result, we show that if f is algebraic and M is homeomorphic to R^(n-1), then M is an entire graph, i.e., there exists a line L in R^n such that M intersects every line parallel L at precisely one point. Finally we will give a number of examples to show that these results are sharp.

- Series
- Combinatorics Seminar
- Time
- Friday, January 29, 2010 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Blair Dowling Sullivan – Oak Ridge National Labs

One of the biggest hurdles in high performance computing today is the analysis of
massive quantities of data. As the size of the datasets grows to petascale (and beyond),
new techniques are needed to efficiently compute meaningful information from the raw data.
Graph-based data (which is ubiquitous in social networks, biological interaction networks, etc) poses additional challenges due to the difficulty of parallelizing many common graph algorithms. A key component in success is the generation of "realistic" random data sets for testing and benchmarking new algorithms.
The R-MAT graph generator introduced by Chakrabarti, Faloutsos, and Zhan (2004) offers a simple, fast method for generating very large directed graphs. One commonly held belief regarding graphs produced by R-MAT
is that they are "scale free"; in other words, their degree distribution follows a
power law as is observed in many real world networks. These properties have made R-MAT a popular choice for generating graphs for use in a variety of research disciplines including graph theoretic benchmarks,
social network analysis, computational biology, and network monitoring.
However, despite its wide usage and elegant, parsimonius design, our recent work
provides the first rigorous mathematical analysis of the degree distributions of
the generated graphs. Applying results from occupancy problems in probability theory, we
derive exact expressions for the degree distributions and other parameters.
We also prove that in the limit (as the number of vertices tends to
infinity), graphs generated with R-MAT have degree distributions that can be expressed as a
mixture of normal distributions. This talk will focus on the techniques used in solving this applied problem in terms of classical "ball and urn" results, including a minor extension of Chistyakov's theorem.

- Series
- CDSNS Colloquium
- Time
- Monday, February 1, 2010 - 11:00 for 1 hour (actually 50 minutes)
- Location
- 269 Skiles
- Speaker
- Peter Kim – University of Utah – kim@math.utah.edu

We improved a computational model of leukemia development from stem cells to terminally differentiated cells by replacing the probabilistic, agent-based model of Roeder et al. (2006) with a system of deterministic, difference equations. The model is based on the relatively recent theory that cancer originates from cancer stem cells that reside in a microenvironment, called the stem cell niche. Depending on a stem cell’s location within the stem cell niche, the stem cell may remain quiescent or begin proliferating. This emerging theory states that leukemia (and potentially other cancers) is caused by the misregulation of the cycle ofproliferation and quiescence within the stem cell niche.Unlike the original agent-based model, which required seven hours per simulation, our model could be numerically evaluated in less than five minutes. The results of our numerical simulations showed that our model closely replicated the average behavior of the original agent-based model. We then extended our difference equation model to a system of age-structured partial differential equations (PDEs), which also reproduced the behavior of the Roeder model. Furthermore, the PDE model was amenable to mathematical stability analysis, which revealed three modes of behavior: stability at 0 (cancer dies out), stability at a nonzero equilibrium (a scenario akin to chronic myelogenous leukemia), and periodic oscillations (a scenario akin to accelerated myelogenous leukemia).The PDE formulation not only makes the model suitable for analysis, but also provides an effective mathematical framework for extending the model to include other aspects, such as the spatial distribution of stem cells within the niche.

- Series
- Analysis Working Seminar
- Time
- Monday, February 1, 2010 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- James Curry – Ga Tech

James Curry will continue his presentation of the paper arXiv:0911.3437, which proves two-weight norm inequalities for a class of dyadic, positive operators.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, February 1, 2010 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Manu O. Platt – Biomedical Engineering (BME), Georgia Tech

Tissue remodeling
involves the activation of proteases, enzymes capable of degrading
the structural proteins of tissue and organs. The implications of
the activation of these enzymes span all organ systems and therefore,
many different disease pathologies, including cancer metastasis.
This occurs when local proteolysis of the structural extracellular
matrix allows for malignant cells to break free from the primary
tumor and spread to other tissues. Mathematical models add value to
this experimental system by explaining phenomena difficult to test at
the wet lab bench and to make sense of complex interactions among the
proteases or the intracellular signaling changes leading to their
expression. The papain family of cysteine proteases, the cathepsins,
is an understudied class of powerful collagenases and elastases
implicated in extracellular matrix degradation that are secreted by
macrophages and cancer cells and shown to be active in the slightly
acidic tumor microenvironment. Due to the tight regulatory
mechanisms of cathepsin activity and their instability outside of
those defined spaces, detection of the active enzyme is difficult to
precisely quantify, and therefore challenging to target
therapeutically. Using valid assumptions that consider these complex
interactions we are developing and validating a system of ordinary
differential equations to calculate the concentrations of mature,
active cathepsins in biological spaces. The system of reactions
considers four enzymes (cathepsins B, K, L, and S, the most studied
cathepsins with reaction rates available), three substrates (collagen
IV, collagen I, and elastin) and one inhibitor (cystatin C) and
comprise more than 30 differential equations with over 50 specified
rate constants. Along with the mathematical model development, we
have been developing new ways to quantify proteolytic activity to
provide further inputs. This predictive model will be a useful tool
in identifying the time scale and culprits of proteolytic breakdown
leading to cancer metastasis and angiogenesis in malignant tumors.

- Series
- Other Talks
- Time
- Tuesday, February 2, 2010 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 249 (Tentatively)
- Speaker
- Doug Ulmer – School of Mathematics, Georgia Tech

- Series
- Research Horizons Seminar
- Time
- Tuesday, February 2, 2010 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Matt Baker – School of Math, Georgia Tech

Hosted by: Huy Huynh and Yao Li

I will discuss some theorems and conjectures in the relatively new
field of arithmetic dynamics, focusing in particular on some methods
from number theory which can be used to study the orbits of points in
algebraic dynamical systems.

- Series
- PDE Seminar
- Time
- Tuesday, February 2, 2010 - 15:10 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Zhiwu Lin – Georgia Tech

Couette flows are shear flows with a linear velocity profile.
Known by Orr in 1907, the vertical velocity of the linearized
Euler equations at Couette flows is known to decay in time, for
L^2 vorticity. It is interesting to know if the perturbed Euler
flow near Couette tends to a nearby shear flow. Such problems
of nonlinear inviscid damping also appear for other stable flows
and are important to understand the appearance of coherent
structures in 2D turbulence. With Chongchun Zeng, we constructed
non-parallel steady flows arbitrarily near Couette flows in
H^s (s<3/2) norm of vorticity. Therefore, the nonlinear inviscid
damping is not true in (vorticity) H^s (s<3/2) norm. We also
showed that in (vorticity) H^s (s>3/2) neighborhood of Couette
flows, the only steady structures (including travelling waves) are
stable shear flows. This suggests that the long time dynamics near
Couette flows in (vorticity) H^s (s>3/2) space might be simpler.
Similar results will also be discussed for the problem of
nonlinear Landau damping in 1D electrostatic plasmas.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, February 3, 2010 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Ilya Nemenman – Emory University

Even the simplest biochemical networks often have more degrees of freedoms than one can (or
should!) analyze. Can we ever hope to do the physicists' favorite trick of coarse-graining,
simplifying the networks to a much smaller set of effective dynamical variables that still
capture the relevant aspects of the kinetics? I will argue then that methods of statistical
physics provide hints at the existence of rigorous coarse-grained methodologies in modeling
biological information processing systems, allowing to identify features of the systems that are
relevant to their functions. While a general solution is still far away, I will focus on a
specific example illustrating the approach. Namely, for a a general stochastic network
exhibiting the kinetic proofreading behavior, I will show that the microscopic parameters of the
system are largely important only to the extent that they contribute to a single aggregate
parameter, the mean first passage time through the network, and the higher cumulants of the
escape time distribution are related to this parameter uniquely. Thus a phenomenological model
with a single parameter does a good job explaining all of the observable data generated by this
complex system.

- Series
- Analysis Seminar
- Time
- Wednesday, February 3, 2010 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Francisco Marcellán – Universidad Carlos III de Madrid

In this talk we will present some recent results about the matrix representation of the multiplication operator in terms of a basis of either orthogonal polynomials (OPUC) or orthogonal Laurent polynomials (OLPUC) with respect to a nontrivial probability measure supported on the unit circle. These are the so called GGT and CMV matrices.When spectral linear transformations of the measure are introduced, we will find the GGT and CMV matrices associated with the new sequences of OPUC and OLPUC, respectively. A connection with the QR factorization of such matrices will be stated. A conjecture about the generator system of such spectral transformations will be discussed.Finally, the Lax pair for the GGT and CMV matrices associated with some special time-depending deformations of the measure will be analyzed. In particular, we will study the Schur flow, which is characterized by a complex semidiscrete modified KdV equation and where a discrete analogue of the Miura transformation appears. Some open problems for time-depending deformations related to spectral linear transformations will be stated.This is a joint work with K. Castillo (Universidad Carlos III de Madrid) and L. Garza (Universidad Autonoma de Tamaulipas, Mexico).

- Series
- School of Mathematics Colloquium
- Time
- Thursday, February 4, 2010 - 11:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Sergei Tabachnikov – Penn State University

Refreshments at 4PM in Skiles 236

The Pentagram map is a projectively natural iteration on
plane polygons. Computer experiments show that the Pentagram map has
quasi-periodic behavior. I shall explain that the Pentagram map is a
completely integrable system whose continuous limit is the Boussinesq
equation, a well known integrable system of soliton type. As a
by-product, I shall demonstrate new configuration theorems of
classical projective geometry.

- Series
- Job Candidate Talk
- Time
- Thursday, February 4, 2010 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Karim Lounici – University of Cambridge

We consider the statistical deconvolution problem where one observes $n$
replications from the model $Y=X+\epsilon$, where $X$ is the unobserved
random signal of interest and where $\epsilon$ is an independent random
error with distribution $\varphi$. Under weak assumptions on the decay of
the Fourier transform of $\varphi$ we derive upper bounds for the
finite-sample sup-norm risk of wavelet deconvolution density estimators
$f_n$ for the density $f$ of $X$, where $f: \mathbb R \to \mathbb R$ is
assumed to be bounded. We then derive lower bounds for the minimax sup-norm
risk over Besov balls in this estimation problem and show that wavelet
deconvolution density estimators attain these bounds. We further show that
linear estimators adapt to the unknown smoothness of $f$ if the Fourier
transform of $\varphi$ decays exponentially, and that a corresponding result
holds true for the hard thresholding wavelet estimator if $\varphi$ decays
polynomially. We also analyze the case where $f$ is a 'supersmooth'/analytic
density. We finally show how our results and recent techniques from
Rademacher processes can be applied to construct global nonasymptotic
confidence bands for the density $f$.

- Series
- SIAM Student Seminar
- Time
- Friday, February 5, 2010 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Linwei Xin – School of Mathematics, Georgia Tech

We are dealing with the following minimization problem: inf {I(\mu): \mu
is a probability measure on R and \int f(x)=t_{0}}, where I(\mu) = \int
(x^2)/2 \mu(dx) + \int\int log|x-y|^{-1} \mu(dx)\mu(dy), f(x) is a bounded
continuous function and t is a given real number. Its motivation and its connection to radom matrices theory will be introduced. We will show that the solution is unique and has a compact support. The possible extension of the
class of f(x) will be discussed.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, February 5, 2010 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Meredith Casey – Georgia Tech

Exact Topic TBA. Talk will be a general survery of branched covers, possibly including covers from the algebraic geometry perspective. In addition we will look at branched coveres in higher dimensions, in the contact world, and my current research interests. This talk will be a general survery, so very little background is assumed.

- Series
- Other Talks
- Time
- Friday, February 5, 2010 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Klaus 1116E
- Speaker
- Jinwoo Shin – Massachusetts Institute of Technology

Refreshments in Room 2222, Klaus Building from 2-3 PM.

Simple, distributed and iterative algorithms, popularly known as the message passing algorithms, have emerged as the architecture of choice for engineered networks as well as cannonical behavioral model for societal and biological networks. Despite their simplicity, message passing algorithms have been surprisingly effective. In this talk, I will try to argue in favor of such algorithms by means of two results in the context of designing efficient medium access in wireless networks and modeling agent behavior in road transportation networks. See the
full abstract,

- Series
- Analysis Working Seminar
- Time
- Monday, February 8, 2010 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- James Curry – Ga Tech

James Curry will finish the discussion of arXiv:0911.3437

- Series
- Algebra Seminar
- Time
- Monday, February 8, 2010 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 171
- Speaker
- Skip Garibaldi – Emory University

The "Exceptionally Simple Theory of Everything" has been the subject of
articles in The New Yorker (7/21/08), Le Monde (11/20/07), the
Financial Times (4/25/09), The Telegraph (11/10/09), an invited talk at
TED (2/08), etc. Despite positive descriptions of the theory in the
popular press, it doesn't work. I'll explain a little of the theory,
the mathematical reasons why it doesn't work, and a theorem (joint work
with Jacques Distler) that says that no similar theory can work. This
talk should be accessible to all graduate students in mathematics.

- Series
- Research Horizons Seminar
- Time
- Tuesday, February 9, 2010 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Ernie Croot – School of Math, Georgia Tech

Hosted by: Huy Huynh and Yao Li

Olof Sisask and myself have produced a new probabilistic
technique for finding `almost periods' of convolutions of subsets of
finite groups. In this talk I will explain how this has allowed us
to give (just recently) new bounds on the length of the longest
arithmetic progression in a sumset A+A.

- Series
- PDE Seminar
- Time
- Tuesday, February 9, 2010 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Ronghua Pan – Georgia Tech – panrh@math.gatech.edu

Darcy's law was observed in the motion of porous medium flows. This talk aims at the mathematical justification on Darcy's law as long time limit from compressible Euler equations with damping. In particularly, we shall showthat any physical solution with finite total mass shall converges in L^1 distance toward the Barenblatt's solution of the same mass for the Porous Medium Equation. The approach will explore the dissipation of the entropy inequality motivated by the second law of thermodynamics. This is a joint work with Feimin Huang and Zhen Wang.

- Series
- Other Talks
- Time
- Wednesday, February 10, 2010 - 10:03 for 1 hour (actually 50 minutes)
- Location
- Klaus 1116W
- Speaker
- Daniel Lokshtanov – Institutt for Informatikk, Universitetet i Bergen

The Subset Sum and Knapsack problems are fundamental NP-complete problems and the pseudo-polynomial time dynamic programming algorithms for them appear in every algorithms textbook. The algorithms require pseudo-polynomial time and space. Since we do not expect polynomial time algorithms for Subset Sum and Knapsack to exist, a very natural question is whether they can be solved in pseudo-polynomial time and polynomial space. In this paper we answer this question affrmatively, and give the first pseudo-polynomial time, polynomial space algorithms for these problems. Our approach is based on algebraic methods and turns out to be useful for several other problems as well. If there is time i will also show how our method can be applied to give polynomial space exact algorithms for the classical Traveling Salesman, Weighted Set Cover and Weighted Steiner Tree problems. Joint work with Jesper Nederlof.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, February 10, 2010 - 11:00 for 1 hour (actually 50 minutes)
- Location
- 255 Skiles
- Speaker
- Steven Ellner – Cornell – spe2@cornell.edu

Emerging diseases have played an important role in the major recent declinesof coral reef cover worldwide. I will present some theoretical efforts aimedat understanding processes of coral disease development and itsconsequences: (1) how the development of coral disease is regulated bymicrobial population interactions within the mucus layer surrounding thecoral, and (2) the effects of a recent fungal epizootic on populations of aCaribbean sea fan coral, focusing on how this species was able to recover tohigh abundance and low disease prevalence. Collaborators on this workinclude John Bruno (UNC-CH); C. Drew Harvell, Laura Jones, and JustinMao-Jones (Cornell), and Kim Ritchie (MOTE Marine Lab).

- Series
- ACO Student Seminar
- Time
- Wednesday, February 10, 2010 - 13:30 for 1 hour (actually 50 minutes)
- Location
- ISyE Executive Classroom
- Speaker
- Daniel Dadush – ISyE ACO, Georgia Tech

The analysis of Chvatal Gomory (CG) cuts and their associated closure for
polyhedra was initiated long ago in the study of integer programming. The
classical results of Chvatal (73) and Schrijver (80) show that the Chvatal
closure of a rational polyhedron is again itself a rational polyhedron. In
this work, we show that for the class of strictly convex bodies the above
result still holds, i.e. that the Chvatal closure of a strictly convex body
is a rational polytope.This is joint work with Santanu Dey (ISyE) and Juan Pablo Vielma (IBM).

- Series
- Analysis Seminar
- Time
- Wednesday, February 10, 2010 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Jeff Geronimo – Georgia Tech

Gasper in his 1971 Annals of Math paper proved that the Jacobi polynomials
satisfy a product formula which generalized the product formula of
Gegenbauer for ultraspherical polynomials. Gasper proved this by showing that
certains sums of triple products of Jacobi polynomials are positive
generalizing results of Bochner who earlier proved a similar results for
ultraspherical polynomials. These results allow a convolution structure for
Jacobi polynomials. We will give a simple proof of Gasper's and Bochner's
results using a Markov operator found by Carlen, Carvahlo, and Loss in their study of the
Kac model in kinetic theory. This is joint work with Eric Carlen and Michael Loss.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, February 12, 2010 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- John Etnyre – Georgia Tech

After, briefly, recalling the definition of contact homology, a powerful but somewhat intractable and still largely unexplored invariant of Legendrian knots in contact structures, I will discuss various ways of constructing more tractable and computable invariants from it. In particular I will discuss linearizations, products, massy products, A_\infty structures and terms in a spectral sequence. I will also show examples that demonstrate some of these invariants are quite powerful. I will also discuss what is known and not known about the relations between all of these invariants.

- Series
- SIAM Student Seminar
- Time
- Friday, February 12, 2010 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 156 (undergraduate computer lab)
- Speaker
- Mitch Keller – School of Mathematics, Georgia Tech

This is an introductory talk to everyone who wants to learn skills in Latex. We will discuss including and positioning graphics and the beamer document class for presentations. A list of other interesting topics will be covered if time permits.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, February 15, 2010 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Lek-Heng Lim – UC Berkeley

Numerical linear algebra is often regarded as a workhorse of scientific and
engineering computing. Computational problems arising from optimization,
partial differential equation, statistical estimation, etc, are usually reduced
to one or more standard problems involving matrices: linear systems, least
squares, eigenvectors/singular vectors, low-rank approximation, matrix
nearness, etc. The idea of developing numerical algorithms for multilinear
algebra is naturally appealing -- if similar problems for tensors of higher
order (represented as hypermatrices) may be solved effectively, then one would
have substantially enlarged the arsenal of fundamental tools in numerical
computations.
We will see that higher order tensors are indeed ubiquitous in applications;
for multivariate or non-Gaussian phenomena, they are usually inevitable.
However the path from linear to multilinear is not straightforward. We will
discuss the theoretical and computational difficulties as well as ways to avoid
these, drawing insights from a variety of subjects ranging from algebraic
geometry to compressed sensing. We will illustrate the utility of such
techniques with our work in cancer metabolomics, EEG and fMRI neuroimaging,
financial modeling, and multiarray signal processing.

- Series
- Algebra Seminar
- Time
- Monday, February 15, 2010 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 171
- Speaker
- David Swinarski – University of Georgia

State polytopes in commutative algebra can be used to
detect the geometric invariant theory (GIT) stability of points in the
Hilbert scheme. I will review the construction of state polytopes and
their role in GIT, and present recent work with Ian Morrison in which
we use state polytopes to estabilish stability for curves of small genus and
low degree, confirming predictions of the minimal model program for the moduli
space of curves.

- Series
- CDSNS Colloquium
- Time
- Monday, February 15, 2010 - 16:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Vladimir Belykh – Nizhny Novgorod University

In this lecture, I will discuss a class of multidimensional maps with one nonlinearity,
often called discrete-time Lurie systems. In the 2-D case, this class includes Lozi map and
Belykh map.
I will derive rigorous conditions for the multidimensional maps to have a generalized
hyperbolic attractor
in the sense of Bunimovich-Pesin. Then, I will show how these chaotic maps can be embedded
into the flow,
and I will give specific examples of three-dimensional piece-wise linear ODEs, generating
this class of hyperbolic attractors.

- Series
- Research Horizons Seminar
- Time
- Tuesday, February 16, 2010 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Doron Lubinsky – School of Mathematics, Georgia Tech

Hosted by: Huy Huynh and Yao Li

Orthogonal Polynomials and their generalizations have a great many
applications in areas ranging from signal processing to random matrices
to combinatorics. We outline a few of the connections, and present some
possible Ph. D Problems

- Series
- PDE Seminar
- Time
- Tuesday, February 16, 2010 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Wilfrid Gangbo – Georgia Tech

Let $\mathbb{H}$ be a Hilbert space and $h: \mathbb{H} \times \mathbb{H} \rightarrow \mathbb{R}$ be such that $h(x, \cdot)$ is uniformly convex and grows superlinearly at infinity, uniformy in $x$. Suppose $U: \mathbb{H} \rightarrow \mathbb{R}$ is strictly convex and grows superlinearly at infinity. We assume that both $H$ and $U$ are smooth. If
$\mathbb{H}$ is of infinite dimension, the initial value problem $\dot x= -\nabla_p h(x, -\nabla U(x)), \; x(0)=\bar x$ is not known to admit a solution. We study a class of parabolic equations on $\mathbb{R}^d$ (and so of infinite dimensional nature), analogous to the previous initial value problem and establish existence of solutions. First, we extend De Giorgi's interpolation method to parabolic equations which are not gradient flows but possess an entropy functional and an underlying Lagrangian. The new fact in the study is that not only the Lagrangian may depend on spatial variables, but it does not induce a metric. These interpolation reveal to be powerful tool for proving convergence of a time discrete algorithm. (This talk is based on a joint work with A. Figalli and T. Yolcu).

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, February 17, 2010 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Raoul-Martin Memmesheimer – Center for Brain Science, Faculty of Arts and Sciences Harvard University

Mean field theory for infinite sparse networks of spiking neurons shows that a balanced state of highly irregular activity arises under a variety of conditions. The state is considered to be a model for the ground state of cortical activity. In the first part, we analytically investigate its irregular dynamics in finite networks keeping track of all individual spike times and the identities of individual neurons. For delayed, purely inhibitory interactions, we show that the dynamics is not chaotic but in fact stable. Moreover, we demonstrate that after long transients the dynamics converges towards periodic orbits and that every generic periodic orbit of these dynamical systems is stable. These results indicate that chaotic and stable dynamics are equally capable of generating the irregular neuronal activity. More generally, chaos apparently is not essential for generating high irregularity of balanced activity, and we suggest that a mechanism different from chaos and stochasticity significantly contributes to irregular activity in cortical circuits.
In the second part, we study the propagation of synchrony in front of a background of irregular spiking activity. We show numerically and analytically that supra-additive dendritic interactions, as recently discovered in single neuron experiments, enable the propagation of synchronous activity even in random networks. This can lead to intermittent events, characterized by strong increases of activity with high-frequency oscillations; our model predicts the shape of these events and the oscillation
frequency. As an example, for the hippocampal region CA1, events with 200Hz oscillations are predicted. We argue that these dynamics provide a plausible explanation for experimentally observed sharp-wave/ripple events.

- Series
- ACO Student Seminar
- Time
- Wednesday, February 17, 2010 - 13:30 for 1 hour (actually 50 minutes)
- Location
- ISyE Executive Classroom
- Speaker
- William T. Trotter – School of Mathematics, Georgia Tech

On-line graph coloring has a rich history, with a very large number of elegant results together with a near equal number of unsolved problems. In this talk, we will briefly survey some of the classic results including: performance on k-colorable graphs and \chi-bounded classes. We will conclude with a sketch of some recent and on-going work, focusing on the analysis of First Fit on particular classes of graphs.

- Series
- ACO Colloquium
- Time
- Wednesday, February 17, 2010 - 16:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 255 (Refreshments at 4pm in Skiles 236)
- Speaker
- David Gamarnik – Professor, M.I.T. – gamarnik@mit.edu

We establish the existence of scaling limits for several combinatorial optimization models on Erdos-Renyi and sparse random regular graphs. For a variety of models, including maximum independent sets, MAX-CUT, coloring and K-SAT, we prove that the optimal value appropriately rescaled, converges to a limit with high probability (w.h.p.), as the size of the underlying graph divergesto infinity. For example, as a special case we prove that the size of a largest independent set in these graphs, normalized by the number of nodes converges to a limit w.h.p. thus resolving an open problem. Our approach is based on developing a simple combinatorial approach to an interpolation method developed recently in the statistical physics literature. Among other things, theinterpolation method was used to prove the existence of the so-called free energy limits for several spin glass models including Viana-Bray and random K-SAT models. Our simpler combinatorial approach allows us to work with the zero temperature case (optimization) directly and extend the approach to many other models. Additionally, using our approach, we establish the large deviationsprinciple for the satisfiability property for constraint satisfaction problems such as coloring, K-SAT and NAE(Not-All-Equal)-K-SAT. The talk will be completely self-contained. No background on random graph theory/statistical physics is necessary. Joint work with Mohsen Bayati and Prasad Tetali

- Series
- Graph Theory Seminar
- Time
- Thursday, February 18, 2010 - 12:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Professor Jason Gao – School of Mathematics and Statistics Carleton University – zgao@math.carleton.ca

A map is a connected graph G embedded in a surface S (a closed 2-manifold) such that all components of S -- G are simply connected regions. A map is rooted if an edge is distinguished together with a direction on the edge and a side of the edge. Maps have been enumerated by both mathematicians and physicists as they appear naturally in the study of representation theory, algebraic geometry, and quantum gravity. In 1986 Bender and Canfield showed that the number of n-edge rooted maps on an orientable surface of genus g is asymptotic to t_g n^{5(g-1)/2}12n^n, (n approaches infinity), where t_g is a positive constant depending only on g. Later it was shown that many families of maps satisfy similar asymptotic formulas in which tg appear as \universal constants". In 1993 Bender et al. derived an asymptotic formula for the num- ber of rooted maps on an orientable surface of genus g with i faces and j vertices. The formula involves a constant tg(r) (which plays the same role as tg), where r is determined by j=i.In this talk, we will review how these asymptotic formulas are obtained using Tutte's recursive approach. Connections with random trees, representation theory, integrable systems, Painleve I, and matrix integrals will also be mentioned. In particular, we will talk aboutour recent results about a simple relation between tg(r) and tg, and asymptotic formulas for the numbers of labeled graphs (of various connectivity)of a given genus. Similar results for non-orientable surfaces will also be discussed.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, February 18, 2010 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Raman Parimala – Department of Mathematics and Computer Science, Emory University

Let k be a p-adic field and K/k function field in one variable
over k. We discuss Hasse principle for existence of rational points
on homogeneous spaces under connected linear algebraic groups.
We illustrate how a positive answer to Hasse principle leads for instance to the result:
every quadratic form in nine variables over K has a nontrivial zero.

- Series
- SIAM Student Seminar
- Time
- Friday, February 19, 2010 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Craig A. Sloane – School of Mathematics, Georgia Tech

This will be an introductory talk about Hardy inequalities. These inequalities are solutions to optimization problems, and their results are well-known. I will survey these results, and discuss some of the techniques used to solve these problems. The applications of Hardy inequalities are broad, from PDE's and mathematical physics to brownian motion. This talk will also serve as a lead-in to my talk at the Analysis seminar next Wednesday in which I discuss some current results that Michael Loss and I have obtained.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, February 19, 2010 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Anh Tran – Georgia Tech

This is part 1 of a two part talk. The second part will continue next week.

I will introduce the AJ conjecture (by Garoufalidis)
which relates the A-polynomial and the colored Jones polynomial of a
knot in the 3-sphere. Then I will verify it for the trefoil and the
figure 8 knots (due to Garoufalidis) and torus knots (due to Hikami) by
explicit calculations.

- Series
- Probability Working Seminar
- Time
- Friday, February 19, 2010 - 15:00 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 169
- Speaker
- Tobias Hurth – Georgia Tech

In my talk, I will present the main results of a recent article by Martin Hairer and Jonathan Mattingly on an ergodic theorem for Markov chains. I will consider Markov chains evolving in discrete time on an abstract, possibly uncountable, state space. Under certain regularity assumptions on the chain's transition kernel, such as the existence of a Foster-Lyapunov function with small level sets (what exactly is meant by that will be thoroughly explained in the talk), one can establish the existence and uniqueness of a stationary distribution. I will focus on a new proof technique for that theorem which relies on a family of metrics on the set of probability measures living on the state space. The main result of my talk will be a strict contraction estimate involving these metrics.

- Series
- Other Talks
- Time
- Saturday, February 20, 2010 - 09:00 for 8 hours (full day)
- Location
- Skiles 249
- Speaker
- Georgia Scientific Computing Symposium – School of Mathematics, Georgia Tech

The purpose of the Georgia Scientific Computing Symposium (GSC 2010) is to provide an opportunity for professors, postdocs and graduate students in the Atlanta area to meet in an informal setting, to exchange ideas, and to highlight local scientific computing research. The one-day symposium is open to the whole research community. The event is free but registration is required.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, February 22, 2010 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Heasoon Park – CSE, Georgia Institute of Technology

Nonnegative Matrix
Factorization (NMF) has attracted much attention during the past
decade as a dimension reduction method in machine learning and data
analysis. NMF provides a lower rank approximation of a nonnegative
high dimensional matrix by factors whose elements are also
nonnegative. Numerous success stories were reported in application
areas including text clustering, computer vision, and cancer class
discovery.
In
this talk, we present novel algorithms for NMF and NTF (nonnegative
tensor factorization) based on the alternating non-negativity
constrained least squares (ANLS) framework. Our new algorithm for NMF
is built upon the block principal pivoting method for the
non-negativity constrained least squares problem that overcomes some
limitations of the classical active set method. The proposed NMF
algorithm can naturally be extended to obtain highly efficient NTF
algorithm for PARAFAC (PARAllel FACtor) model. Our algorithms
inherit the convergence theory of the ANLS framework and can easily
be extended to other NMF formulations such as sparse NMF and NTF with
L1 norm constraints. Comparisons of algorithms using various data
sets show that the proposed new algorithms outperform existing ones
in computational speed as well as the solution quality.
This
is a joint work with Jingu Kim and Krishnakumar Balabusramanian.

- Series
- Analysis Working Seminar
- Time
- Monday, February 22, 2010 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Michael Lacey – Georgia Tech

We will start a discussion of arXiv:1001.4043, which characterizes the two weight inequality for the Hilbert transform, including the statement of the theorem, and some examples of how this question arises. Joint work with Ignacio Uriate-Tuero, and Eric Sawyer.

- Series
- Research Horizons Seminar
- Time
- Tuesday, February 23, 2010 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Prasad Tetali – Professor, School of Mathematics and School of Computer Science

Hosted by: Huy Huynh and Yao Li

Sampling from and approximately counting the size of a large set
of combinatorial structures has contributed to a renaissance in research
in finite Markov chains in the last two decades.
Applications are wide-ranging from sophisticated card shuffles,
deciphering simple substitution ciphers (of
prison inmates in the California state prison), estimating the volume of
a high-dimensional convex body,
and to understanding the speed of Gibbs sampling heuristics in
statistical physics. More recent applications include rigorous estimates
on J.M. Pollard's (1979) classical Rho and Kangaroo algorithms for the
discrete logarithm problem in finite cyclic groups.
The lecture will be a brief (mostly self-contained) introduction to the
Markov Chain Monte Carlo (MCMC) methodology and applications, and will
include some open problems.

- Series
- Analysis Seminar
- Time
- Wednesday, February 24, 2010 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Craig Sloane – Georgia Tech

We prove a sharp Hardy inequality for fractional integrals for functions that are supported in a convex domain. The constant is the same as the one for the half-space and hence our result settles a recent conjecture of Bogdan and Dyda. Further, the Hardy term in this inequality is stronger than the one in the classical case. The result can be extended as well to more general domains

- Series
- Other Talks
- Time
- Wednesday, February 24, 2010 - 16:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Skip Garibaldi – Department of Mathematics and Computer Science

Dr. Skip Garibaldi, Emory University's Winship Distinguished Professor,
will make a presentation on Mathematics of the Lottery. He will discuss his
expository article: "Finding good bets in the lottery, and why you shouldn't take them"
recently published in the American Mathematical Monthly, Volume 117 (2010) 3-26.

- Series
- Stochastics Seminar
- Time
- Thursday, February 25, 2010 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Stanislav Molchanov – UNC Charlotte

The talk will present several
limit theorems for the supercritical colony of the particles with masses. Reaction-diffusion
equations responsible for the spatial distribution of the species contain
the usual random death, birth and migration processes. The evolution
of the mass of the individual particle includes (together with the diffusion)
the mitosis: the splitting of the mass between the two offspring.
The last process leads to the new effects. The limit theorems give the
detailed picture of the space –mass distribution of the particles
in the bulk of the moving front of the population.

- Series
- Geometry Topology Seminar
- Time
- Friday, February 26, 2010 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Qi Chen – Winston-Salem State University

For every quantum group one can define two invariants of 3-manifolds:the WRT invariant and the Hennings invariant. We will show that theseinvariants are equivalentfor quantum sl_2 when restricted to the rational homology 3-spheres.This relation can be used to solve the integrality problem of the WRT invariant.We will also show that the Hennings invariant produces integral TQFTsin a more natural way than the WRT invariant.

- Series
- Probability Working Seminar
- Time
- Friday, February 26, 2010 - 15:00 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 169
- Speaker
- Tobias Hurth – Georgia Tech

This is a continuation of last week's talk.

- Series
- Combinatorics Seminar
- Time
- Friday, February 26, 2010 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Rui Xu – Department of Mathematics, University of West Georgia

The map coloring problem is one of the major catalysts of the tremendous
development of graph theory. It was observed by Tutte that the problem of
the face-coloring of an planar graph can be formulated in terms of integer
flows of the graph. Since then the topic of integer flow has been one of the
most attractive in graph theory. Tutte had three famous fascinating flow
conjectures: the 3-flow conjecture, the 4-flow conjecture and the 5-flow
conjecture. There are some partial results for these three conjectures. But
in general, all these 3 conjectures are open.
Group connectivity is a generalization of integer flow of graphs. It
provides us with contractible flow configurations which play an important
role in reducing the graph size for integer flow problems, it is also
related to all generalized Tutte orientations of graphs. In this talk, I
will present an introduction and survey on group connectivity of graphs as
well as some open problems in this field.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, March 1, 2010 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- James G. Nagy – Mathematics and Computer Science, Emory University

Large-scale inverse problems arise in a variety of importantapplications in image processing, and efficient regularization methodsare needed to compute meaningful solutions. Much progress has beenmade in the field of large-scale inverse problems, but many challengesstill remain for future research. In this talk we describe threecommon mathematical models including a linear, a separable nonlinear,and a general nonlinear model. Techniques for regularization andlarge-scale implementations are considered, with particular focusgiven to algorithms and computations that can exploit structure in theproblem. Examples will illustrate the properties of these algorithms.

- Series
- Analysis Working Seminar
- Time
- Monday, March 1, 2010 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Michael Lacey – GT

We start the proof of arXiv:1001.4043,
which characterizes the two weight inequality for the Hilbert
transform. This session will be devoted to necessity of the Poisson A_2 condition and the Energy Condition. Joint work with Ignacio Uriate-Tuero, and
Eric Sawyer.

- Series
- Algebra Seminar
- Time
- Monday, March 1, 2010 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 171
- Speaker
- Doug Ulmer – Georgia Tech

It turns out to be very easy to write down interesting points on the
classical Legendre elliptic curve y^2=x(x-1)(x-t) and show that they
generate a group of large rank. I'll give some basic background,
explain the construction, and discuss related questions which would
make good thesis projects (both MS and PhD).

- Series
- Other Talks
- Time
- Monday, March 1, 2010 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Howey N110
- Speaker
- Kevin Mitchell – University of California, Merced

Hamiltonian systems typically exhibit a mixture of chaos and regularity, complicating any scheme to partition phase space and extract a symbolic description of the dynamics. In particular, the dynamics in the vicinity of stable islands can exhibit extremely complicated topology. We present an approach to extracting symbolic dynamics in such systems using networks of nested heteroclinic tangles-- fundamental geometric objects that organize phase space transport. These tangles can be used to progressively approximate the behavior in the vicinity of stable island chains. The net result is a symbolic approximation to the dynamics, and an associated phase-space partition, that includes the influence of stable islands. The utility of this approach is illustrated by examining two applications in atomic physics -- the chaotic escape of ultracold atoms from an atomic trap and the chaotic ionization of atoms in external fields.

- Series
- Research Horizons Seminar
- Time
- Tuesday, March 2, 2010 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Michael Lacey – School of Math, Georgia Tech

Hosted by: Huy Huynh and Yao Li

The Hilbert transform is a foundational transform, with deep connections to
electrical charge, and analyticity. The `two weight inequality for the
Hilbert transform' concerns the most general setting in which the Hilbert
transform admits a (weighted) L^2 inequality. We will give a couple of
(surprising?) ways that this question arises. And we will indicate the
surprise that is behind the recent description of all setting in which the
two weight inequality holds.

- Series
- PDE Seminar
- Time
- Tuesday, March 2, 2010 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Marius Paicu – Université Paris-Sud

We consider the three dimensional Navier-Stokes equations with a large initial data and we prove the existence of a global smooth solution. The main feature of the initial data is that it varies slowly in the vertical direction and has a norm which blows up as the small parameter goes to zero. Using the language of geometrical optics, this type of initial data can be seen as the ``ill prepared" case. Using analytical-type estimates and the special structure of the nonlinear term of the equation we obtain the existence of a global smooth solution generated by this large initial data. This talk is based on a work in collaboration with J.-Y. Chemin and I. Gallagher and on a joint work with Z. Zhang.

- Series
- Analysis Working Seminar
- Time
- Wednesday, March 3, 2010 - 13:46 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Michael Lacey – GT

We start the sufficiency proof of arXiv:1001.4043,
which
characterizes the two weight inequality for the Hilbert
transform. This session will be devoted to the martingale methods employed. Joint work with Ignacio
Uriate-Tuero, and
Eric Sawyer.

- Series
- Analysis Seminar
- Time
- Wednesday, March 3, 2010 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Doron Lubinsky – Georgia Tech

Let mu be a measure with compact support, with orthonormal polynomials {p_{n}} and associated reproducing kernels {K_{n}}. We show that bulk universality holds in measure in {x:mu'(x)>0}. The novelty is that there are no local or global conditions on the measure. Previous results have required regularity as a global condition, and a Szego condition as a local condition.As a consequence, for a subsequence of integers, universality holds for a.e. x. Under additional conditions on the measure, we show universality holds in an L_{p} sense for all finite p>0.

- Series
- Other Talks
- Time
- Wednesday, March 3, 2010 - 19:30 for 1 hour (actually 50 minutes)
- Location
- LeCraw Auditorium, College of Management, Room 100
- Speaker
- Nalini Nadkarni – Evergreen State College

Hosted by Academic Affairs Honors Program in collaboration with the College of Sciences.

To watch a 15-minute presentation by Dr. Nadkarni see the
YouTube link.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, March 4, 2010 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Maarten V. de Hoop – Department of Mathematics, Purdue University

Much research in modern, quantitative seismology is motivated -- on
the one hand -- by the need to understand subsurface structures and
processes on a wide range of length scales, and -- on the other hand
-- by the availability of ever growing volumes of high fidelity
digital data from modern seismograph networks or multicomponent
acquisition systems developed for hydro-carbon exploration, and access
to increasingly powerful computational facilities. We discuss
(elastic-wave) inverse scattering of reflection seismic data,
wave-equation tomography, and their interconnection using techniques
from microlocal analysis and applied harmonic analysis. We introduce a
multi-scale approach and present a framework of partial reconstruction
in connection with limited boundary acquisition geometry. The formation of caustics
leads to one of the complications which will be discussed. We illustrate various
aspects of this research program with examples from global seismology and mineral
physics coupled to thermo-chemical convection.

- Series
- Stochastics Seminar
- Time
- Thursday, March 4, 2010 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Dr Juri Lember – Tartu University, Estonia – juri.lember@ut.ee

Abstract: We consider the hidden Markov model, where the dynamic of theprocess is modelled by a latent Markov chain Y and the observations X aresuch that: 1) given the realization of Y, the observations areindependent; 2) the distribution of the i-th observations (X_i) depends onthe i-th element of the Y (Y_i), only.The segmentation problem consists of estimating the underlying realization(path) of Y given the n observation. Usually the realization with maximumlikelihood, the so called Viterbi alignment is used. On the other hand, itis easy to see that the Viterbi alignment does not minimize the expectednumber of misclassification errors.We consider the segmentation problem in the framework of statisticallearning. This unified risk-based approach helps to analyse many existingalignments as well as defining many new ones. We also study theasymptotics of the risks and infinite alignments.

- Series
- SIAM Student Seminar
- Time
- Friday, March 5, 2010 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Yao Li – Georgia Tech

Last semester, I reviewed the relation between dynamical system,
Fokker-Planck equation and thermodynamics (free energy and Gibbs
distribution). This time let's go further. I will review the geometric
properties of a kind of dissipative evolution equations. I will explain
why this kind of evolutionary equations (Fokker-Planck equation,
nonlinear Fokker-Planck equation, Porous medium equation) are the
gradient flow of some energy function on a Riemannian manifold --
2-Wasserstein metric space.

- Series
- Geometry Topology Working Seminar
- Time
- Friday, March 5, 2010 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Anh Tran – Georgia Tech

I will explain another approach to the conjecture and in particular,
study it for 2-bridge knots. I will give the proof of the conjecture
for a very large class of 2-bridge knots which includes twist knots and
many more (due to Le). Finally, I will mention a little bit about the
weak version of the conjecture as well as some relating problems.

- Series
- Combinatorics Seminar
- Time
- Friday, March 5, 2010 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Asaf Shapira – School of Mathematics, Georgia Tech

Let a_1,...,a_k satisfy a_1+...+a_k=1 and suppose a k-uniform hypergraph on n
vertices satisfies the following property; in any partition of its vertices into k
sets A_1,...,A_k of sizes a_1*n,...,a_k*n, the number of edges intersecting
A_1,...,A_k is the number one would expect to find in a random k-uniform hypergraph.
Can we then infer that H is quasi-random? We show that the answer is negative if and
only if a_1=...=a_k=1/k. This resolves an open problem raised in 1991 by Chung and
Graham [J. AMS '91].
While hypergraphs satisfying the property corresponding to a_1=...=a_k=1/k are not
necessarily quasi-random, we manage to find a characterization of the hypergraphs
satisfying this property. Somewhat surprisingly, it turns out that (essentially)
there is a unique non quasi-random hypergraph satisfying this property. The proofs
combine probabilistic and algebraic arguments with results from the theory of
association schemes.
Joint work with Raphy Yuster

- Series
- Other Talks
- Time
- Saturday, March 6, 2010 - 09:00 for 8 hours (full day)
- Location
- Skiles 269
- Speaker
- SIAM Student Conference – School of Mathematics, Georgia Tech

The SIAM Student Chapter at Georgia Tech will be hosting this conference. It is an extension of the ACES Workshop which has been held yearly by the universities of Auburn, Clemson, Emory, and South Carolina since 2006. As with the ACES Workshop, this conference is an opportunity for graduate students to present their research in applied mathematics and related fields as well as to meet with other graduate students from different universities and departments. See the conference site for more details.

- Series
- Other Talks
- Time
- Saturday, March 6, 2010 - 19:00 for 1 hour (actually 50 minutes)
- Location
- Instructional Center Room 103
- Speaker
- Art Benjamin – Harvey Mudd College

The speaker has combined his two loves to create a dynamic presentation called "Mathemagics," suitable for all audiences, where he demonstrates and explains his secrets for performing rapid mental calculations faster than a calculator. Reader's Digest calls him "America's Best Math Whiz". He has presented his high energy talk for thousands of groups throughout the world. This event is free but reservations are required. The signup form will be available before 5pm on February 25.
See details about the speaker.

- Series
- Other Talks
- Time
- Monday, March 8, 2010 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Room 129, Global Learning Center (behind the GA Tech Hotel)
- Speaker
- Christine Franklin – University of Georgia

For more information, see the <A href="/~rohrs/FranklinColloquium.pdf">flyer</a>.

Statistics is now a part of the K-12 curriculum (including elementary school) and there is much activity in the area of statistics education. This colloquium is intended for any and all faculty, staff, and students, who are interested in, have taught, or have children in k-12 schools.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, March 8, 2010 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Chun Liu – Penn State/IMA

Almost all models for complex fluids can be fitted into the energetic variational framework. The advantage of the approach is the revealing/focus of the competition between the kinetic energy and the internal "elastic" energies. In this talk, I will discuss two very different engineering problems: free interface motion in Newtonian fluids and viscoelastic materials. We will illustrate the underlying connections between the problems and their distinct properties. Moreover, I will present the analytical results concerning the existence of near equilibrium solutions of these problems.

- Series
- Algebra Seminar
- Time
- Monday, March 8, 2010 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 171
- Speaker
- Mihran Papikian – Penn State

We discuss some arithmetic properties of modular varieties
of D-elliptic sheaves, such as the existence of rational points or
the structure of their "fundamental domains" in the Bruhat-Tits
building. The notion of D-elliptic sheaf is a generalization of the
notion of Drinfeld module. D-elliptic sheaves and their moduli
schemes were introduced by Laumon, Rapoport and Stuhler in their
proof of certain cases of the Langlands conjecture over function
fields.

- Series
- Research Horizons Seminar
- Time
- Tuesday, March 9, 2010 - 12:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Heinrich Matzinger – Professor, School of Mathematics

Hosted by: Huy Huynh and Yao Li

The Scenery Reconstruction Problem consists in trying to reconstruct
a coloring of the integers given only the observations made by
a random walk. For this we consider a random walk S and
a coloring of the integers X. At time $t$ we observe
the color $X(S(t))$. The coloring is i.i.d. and we show that
given only the sequence of colors
$$X(S(0)),X(S(1)),X(S(2)),...$$
it is possible to reconstruct $X$ up to translation
and reflection. The solution depends on the property of the
random walk and the distribution of the coloring.
Longest Common Subsequences (LCS) are widely used in genetics.
If we consider two sequences X and Y, then a common subsequence
of X and Y is a string which is a subsequence of X and of Y at the same
time. A Longest Common Subsequence of X and Y is a common
subsequence of X and Y of maximum length. The problem of the asymptotic
order of the flucutation for the LCS of independent random
strings has been open for decades. We have now been able to
make progress on this problem for several important cases.
We will also show the connection to the Scenery Reconstruction
Problem.

- Series
- PDE Seminar
- Time
- Tuesday, March 9, 2010 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Bob Pego – Carnegie Mellon University

A classic story of nonlinear science started with the
particle-like
water wave that Russell famously chased on horseback in 1834. I will
recount progress regarding the robustness of solitary waves in
nonintegrable model systems such as FPU lattices, and discuss progress
toward a proof (with Shu-Ming Sun) of spectral stability of small
solitary waves for the 2D Euler equations for water of finite depth
without surface tension.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, March 10, 2010 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Yuri Bakhtin – Georgia Tech

I will consider a class of mathematical models of decision
making. These models are based on dynamics in the neighborhood of
unstable equilibria and involve random perturbations due to small
noise. I will report results on the vanishing noise limit for these
systems, providing precise predictions about the statistics of
decision making times and sequences of unstable equilibria visited by
the process. Mathematically, the results are based on the analysis of
random Poincare maps in the neighborhood of each equilibrium point. I
will also discuss some experimental data.

- Series
- Other Talks
- Time
- Wednesday, March 10, 2010 - 16:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Matt Baker – Georgia Tech

Join math club for Dr. Baker's mathematical magic show.

- Series
- Dissertation Defense
- Time
- Thursday, March 11, 2010 - 11:00 for 1.5 hours (actually 80 minutes)
- Location
- Van Leer Building Room W225
- Speaker
- Shannon Bishop – School of Mathematics, Georgia Tech

This thesis addresses four topics in the area of applied harmonic analysis. First, we show that the affine densities of separable wavelet frames affect the frame properties. In particular, we describe a new relationship between the affine densities, frame bounds and weighted admissibility constants of the mother wavelets of pairs of separable wavelet frames. This result is also extended to wavelet frame sequences. Second, we consider affine pseudodifferential operators, generalizations of pseudodifferential operators that model wideband wireless communication channels. We find two classes of Banach spaces, characterized by wavelet and ridgelet transforms, so that inclusion of the kernel and symbol in appropriate spaces ensures the operator if Schatten p-class. Third, we examine the Schatten class properties of pseudodifferential operators. Using Gabor frame techniques, we show that if the kernel of a pseudodifferential operator lies in a particular mixed modulation space, then the operator is Schatten p-class. This result improves existing theorems and is sharp in the sense that larger mixed modulation spaces yield operators that are not Schatten class. The implications of this result for the Kohn-Nirenberg symbol of a pseudodifferential operator are also described. Lastly, Fourier integral operators are analyzed with Gabor frame techniques. We show that, given a certain smoothness in the phase function of a Fourier integral operator, the inclusion of the symbol in appropriate mixed modulation spaces is sufficient to guarantee that the operator is Schatten p-class.

- Series
- Stochastics Seminar
- Time
- Thursday, March 11, 2010 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Evarist Giné – University of Connecticut

The almost sure rate of convergence in the sup norm for linear wavelet density estimators is obtained, as well as a central limit theorem for the distribution functions based on these estimators. These results are then applied to show that the hard thresholding wavelet estimator of Donoho, Johnstone, Kerkyacharian and Picard (1995) is adaptive in sup norm to the smoothness of a density. An alternative adaptive estimator combining Lepski's method with Rademacher complexities will also be described. This is joint work with Richard Nickl.

- Series
- ACO Seminar
- Time
- Thursday, March 11, 2010 - 16:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Lisa Fleischer – Professor, Dartmouth College

We look at problems of scheduling jobs to machines when the processing time of a job is machine dependent. Common objectives in this framework are to minimize the maximum load on a machine, or to minimize the average completion time of jobs. These are well-studied problems. We consider the related problem of trying to select a subset of machines to use to minimize machine costs subject to bounds on the maximum load or average completion time of the corresponding schedule. These problems are NP-hard and include set-cover as a special case. Thus we fo