Seminars and Colloquia by Series

Avoiding Grid-Points in Affine or Linear Spaces of Small Dimension

Series
Combinatorics Seminar
Time
Thursday, September 25, 2008 - 12:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Hanno LefmannTechnical 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.

A Turning Point Theory for Difference Equations

Series
Research Horizons Seminar
Time
Wednesday, September 24, 2008 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Jeff GeronimoSchool 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.

Algebraic models in systems biology

Series
Mathematical Biology Seminar
Time
Wednesday, September 24, 2008 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Reinhard LaubenbacherVirginia 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.

Segregation of Granular Materials - Experiments, Modeling, Analysis and Simulations

Series
PDE Seminar
Time
Tuesday, September 23, 2008 - 15:15 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Michael ShearerDepartment 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.

Correlation Decay and Deterministic Approximation Algorithms

Series
ACO Student Seminar
Time
Tuesday, September 23, 2008 - 15:00 for 1 hour (actually 50 minutes)
Location
ISyE executive classroom
Speaker
Prasad TetaliSchool 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.

Spectral invariants, the energy-capacity inequality, and the non-squeezing theorem

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 UsherDepartment 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.

The HOMFLY polynomial, the trilogarithm and zeta(3)

Series
Geometry Topology Seminar
Time
Monday, September 22, 2008 - 14:30 for 2 hours
Location
Room 322, Boyd Graduate Studies UGA
Speaker
Stavros GaroufalidisSchool 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.

Horn Conjecture for finite von Neumann algebras

Series
Analysis Seminar
Time
Monday, September 22, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Wing Suet LiSchool 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!

Numerical Simulations with Uncertainty - Prediction and Estimation

Series
Applied and Computational Mathematics Seminar
Time
Monday, September 22, 2008 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Dongbin XiuDivision 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.

On a hypergraph generalization of the Balog-Szemeredi-Gowers Theorem

Series
Combinatorics Seminar
Time
Friday, September 19, 2008 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Evan BorensteinSchool 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.

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