Seminars and Colloquia Schedule

Discrete Mathematical Biology Working Seminar

Series
Other Talks
Time
Monday, October 31, 2011 - 11:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 114
Speaker
Will Perkins – Georgia Tech
A discussion of the Moulton et all (2000) paper "Metrics on RNA Secondary Structures."

Fast Spectral-Galerkin Methods for High-Dimensional PDEs and Applications to the electronic Schrodinger equation

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 31, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jie Shen – Purdue University, Department of Mathematics
Many scientific, engineering and financial applications require solving high-dimensional PDEs. However, traditional tensor product based algorithms suffer from the so called "curse of dimensionality".We shall construct a new sparse spectral method for high-dimensional problems, and present, in particular,  rigorous error estimates as well as efficient numerical algorithms for  elliptic equations in both bounded and unbounded domains.As an application, we shall use the proposed sparse spectral method to solve the N-particle electronic  Schrodinger equation.

Joint Emory-Tech-UGA Seminar - Small entropy surface homeomorphisms

Series
Geometry Topology Seminar
Time
Monday, October 31, 2011 - 14:30 for 1 hour (actually 50 minutes)
Location
UGA Boyd 302
Speaker
Dan Margalit – Ga Tech

Note that this talk is on the UGA campus.

To every homeomorphism of a surface, we can attach a positive real number, the entropy. We are interested in the question of what these homeomorphisms look like when the entropy is positive, but small. We give several perspectives on this problem, considering it from the complex analytic, surface topological, 3-manifold theoretical, and numerical points of view. This is joint work with Benson Farb and Chris Leininger.

Joint Emory-Tech-UGA Seminar - A contact invariant in sutured monopole homology

Series
Geometry Topology Seminar
Time
Monday, October 31, 2011 - 16:00 for 1 hour (actually 50 minutes)
Location
UGA Boyd 302
Speaker
John Baldwin – Princeton

Note that this talk is on the UGA campus.

A contact manifold with boundary naturally gives rise to a sutured manifold, as defined by Gabai. Honda, Kazez and Matic have used this relationship to define an invariant of contact manifolds with boundary in sutured Floer homology, a Heegaard-Floer-type invariant of sutured manifolds developed by Juhasz. More recently, Kronheimer and Mrowka have defined an invariant of sutured manifolds in the setting of monopole Floer homology. In this talk, I'll describe work-in-progress to define an invariant of contact manifolds with boundary in their sutured monopole theory. If time permits, I'll talk about analogues of Juhasz' sutured cobordism maps and the Honda-Kazez-Matic gluing maps in the monopole setting. Likely applications of this work include an obstruction to the existence of Lagrangian cobordisms between Legendrian knots in S^3. Other potential applications include the construction of a bordered monopole theory, following an outline of Zarev. This is joint work with Steven Sivek.

Hilbert-Kunz multiplicities

Series
Algebra Seminar
Time
Monday, October 31, 2011 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Florian Enescu – Georgia State University
The talk will discuss the notion of Hilbert-Kunz multiplicity, presenting its general theory and listing some of the outstanding open problems together with recent progress on them.

A microscopic derivation of Ginzburg-Landau theory

Series
Math Physics Seminar
Time
Tuesday, November 1, 2011 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Rupert Frank – Dept. of Math, Princeton University
We describe the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit is semiclassical in nature, and semiclassical analysis, with minimal regularity assumptions, plays an important part in our proof. The talk is based on joint work with C. Hainzl, R. Seiringer and J. P. Solovej.

Global existence results for water waves

Series
PDE Seminar
Time
Tuesday, November 1, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Pierre Germain – New York University, Courant Institute of Mathematical Sciences
I will describe results of global existence and scattering for water waves (inviscid, irrotational), in the case of small data. I will examine two physical settings: gravity, but no capillarity; or capillarity, but no gravity. The proofs rely on the space-time resonance method, which I will briefly present. This is joint work with Nader Masmoudi and Jalal Shatah.

Vectors, Sampling and Massive Data

Series
ACO Distinguished Lecture
Time
Tuesday, November 1, 2011 - 16:30 for 1 hour (actually 50 minutes)
Location
Klaus 1116
Speaker
Ravi Kannan – Microsoft Research India

There will be a reception in the Atrium of the Klaus building at 4PM.

Modeling data as high-dimensional (feature) vectors is a staple in Computer Science, its use in ranking web pages reminding us again of its effectiveness. Algorithms from Linear Algebra (LA) provide a crucial toolkit. But, for modern problems with massive data, these algorithms may take too long. Random sampling to reduce the size suggests itself. I will give a from-first-principles description of the LA connection, then discuss sampling techniques developed over the last decade for vectors, matrices and graphs. Besides saving time, sampling leads to sparsification and compression of data. Speaker's bio

Getting in shape with eigenvalues

Series
Research Horizons Seminar
Time
Wednesday, November 2, 2011 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Evans Harrell – School of Mathematics, Georgia Tech
Eigenvalues of linear operators often correspond to physical observables; for example they determine the energy levels in quantum mechanics and the frequencies of vibration in acoustics. Properties such as the shape of a system are encoded in the the set of eigenvalues, known as the "spectrum," but in subtle ways. I'll talk about some classic theorems about how geometry and topology show up in the spectrum of differential operators, and then I'll present some recent work, with connections to physical models such as quantum waveguides, wires, and graphs.

Rays and Souls in Von Mangoldt Planes

Series
Geometry Topology Student Seminar
Time
Wednesday, November 2, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Eric Choi – Emory University
Knowledge of rays and critical points of infinity in von Mangoldt planes can be applied to understanding the structure of open complete manifolds with lower radial curvature bounds. We will show how the set of souls is computed for every von Mangoldt plane of nonnegative curvature. We will also make some observations on the structure of the set of critical points of infinity for von Mangoldt planes with negative curvature.

Bernstein's problem on weighted polynomial approximation

Series
Analysis Seminar
Time
Wednesday, November 2, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alexei Poltoratski – Texas A&M
The problem of weighted polynomial approximation of continuousfunctionson the real line was posted by S. Bernstein in 1924. It asks for adescription of theset of weights such that polynomials are dense in the space of continuousfunctions withrespect to the corresponding weighted uniform norm. Throughout the 20thcentury Bernstein's problem was studied by many prominent analysts includingAhkiezer, Carleson, Mergelyan andM. Riesz.In my talk I will discuss some of the complex analytic methods that can beapplied in Bernstein's problem along with a recently found solution.

Athens-Atlanta Number Theory Seminar - Lecture 1 - Maximal varieties over finite fields

Series
Other Talks
Time
Wednesday, November 2, 2011 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jared Weinstein – Institute for Advanced Study and Boston University
This is joint work with Mitya Boyarchenko. We construct a special hypersurface X over a finite field, which has the property of "maximality", meaning that it has the maximum number of rational points relative to its topology. Our variety is derived from a certain unipotent algebraic group, in an analogous manner as Deligne-Lusztig varieties are derived from reductive algebraic groups. As a consequence, the cohomology of X can be shown to realize a piece of the local Langlands correspondence for certain wild Weil parameters of low conductor.

Athens-Atlanta Number Theory Seminar - Lecture 2 - Random Dieudonee modules and the Cohen-Lenstra conjectures

Series
Other Talks
Time
Wednesday, November 2, 2011 - 17:15 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
David Brown – Department of Mathematics and Computer Science, Emory University
Knowledge of the distribution of class groups is elusive -- it is not even known if there are infinitely many number fields with trivial class group. Cohen and Lenstra noticed a strange pattern -- experimentally, the group \mathbb{Z}/(9) appears more often than \mathbb{Z{/(3) x \mathbb{Z}/(3) as the 3-part of the class group of a real quadratic field \Q(\sqrt{d}) - and refined this observation into concise conjectures on the manner in which class groups behave randomly. Their heuristic says roughly that p-parts of class groups behave like random finite abelian p-groups, rather than like random numbers; in particular, when counting one should weight by the size of the automorphism group, which explains why \mathbb{Z}/(3) x \mathbb{Z}/(3) appears much less often than \mathbb{Z}/(9) (in addition to many other experimental observations). While proof of the Cohen-Lenstra conjectures remains inaccessible, the function field analogue -- e.g., distribution of class groups of quadratic extensions of \mathbb{F}_p(t) -- is more tractable. Friedman and Washington modeled the \el$-power part (with \ell \neq p) of such class groups as random matrices and derived heuristics which agree with experiment. Later, Achter refined these heuristics, and many cases have been proved (Achter, Ellenberg and Venkatesh). When $\ell = p$, the $\ell$-power torsion of abelian varieties, and thus the random matrix model, goes haywire. I will explain the correct linear algebraic model -- Dieudone\'e modules. Our main result is an analogue of the Cohen-Lenstra/Friedman-Washington heuristics -- a theorem about the distributions of class numbers of Dieudone\'e modules (and other invariants particular to \ell = p). Finally, I'll present experimental evidence which mostly agrees with our heuristics and explain the connection with rational points on varieties.

Limit theorems for geometrical characteristics of Gaussian excursion sets

Series
Stochastics Seminar
Time
Thursday, November 3, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alexey Shashkin – Moscow State University
Excursion sets of stationary random fields have attracted much attention in recent years.They have been applied to modeling complex geometrical structures in tomography, astro-physics and hydrodynamics. Given a random field and a specified level, it is natural to studygeometrical functionals of excursion sets considered in some bounded observation window.Main examples of such functionals are the volume, the surface area and the Euler charac-teristics. Starting from the classical Rice formula (1945), many results concerning calculationof moments of these geometrical functionals have been proven. There are much less resultsconcerning the asymptotic behavior (as the window size grows to infinity), as random variablesconsidered here depend non-smoothly on the realizations of the random field. In the talk wediscuss several recent achievements in this domain, concentrating on asymptotic normality andfunctional central limit theorems.

Spectral gaps and completeness of complex exponentials

Series
School of Mathematics Colloquium
Time
Thursday, November 3, 2011 - 23:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alexei Poltoratski – Texas A&M
One of the basic problems of Harmonic analysis is to determine ifa given collection of functions is complete in a given Hilbert space. Aclassical theorem by Beurling and Malliavin solved such a problem in thecase when the space is $L^2$ on an interval and the collection consists ofcomplex exponentials. Two closely related problems, the so-called Gap andType Problems, studied by Beurling, Krein, Kolmogorov, Levinson, Wiener andmany others, remained open until recently.In my talk I will  present solutions to the Gap and Type problems anddiscuss their connectionswith adjacent fields.

Examples of negatively curved manifold (after Ontaneda)

Series
Geometry Topology Working Seminar
Time
Friday, November 4, 2011 - 14:05 for 2 hours
Location
Skiles 006
Speaker
Igor Belegradek – Georgia Tech
This is the first in the series of two talks aimed to discuss a recent work of Ontaneda which gives a poweful method of producing negatively curved manifolds. Ontaneda's work adds a lot of weight to the often quoted Gromov's prediction that in a sense most manifolds (of any dimension) are negatively curved.

Decomposition of Sparse Graphs into Forests and a Graph with Bounded Degree

Series
Combinatorics Seminar
Time
Friday, November 4, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Douglas B. West – University of Illinois
Say that a graph with maximum degree at most $d$ is {\it $d$-bounded}.  For$d>k$, we prove a sharp sparseness condition for decomposition into $k$ forestsand a $d$-bounded graph.  The condition holds for every graph with fractionalarboricity at most $k+\FR d{k+d+1}$.  For $k=1$, it also implies that everygraph with maximum average degree less than $2+\FR{2d}{d+2}$ decomposes intoone forest and a $d$-bounded graph, which contains several earlier results onplanar graphs.

Atlanta Lecture Series in Combinatorics and Graph Theory IV

Series
Other Talks
Time
Saturday, November 5, 2011 - 09:30 for 1 hour (actually 50 minutes)
Location
Petit Science Center, Room 124, Georgia State University
Speaker
Featured Speaker Bela Bollobas – Cambridge University and University of Memphis

Please contact Guantao Chen, <a href="mailto:gchen@gsu.edu">gchen@gsu.edu</a> if you are interested in participating this mini-conference.

Emory University, the Georgia Institute of Technology and Georgia State University, with support from the National Security Agency and the National Science Foundation, are hosting a series of 9 mini-conferences from November 2010 - April 2013. The fourth in the series will be held at Georgia State University on November 5-6, 2011. This mini-conference's featured speaker is Dr. Bela Bollobas, who will give two one-hour lectures. Additionally, there will be five one-hour talks and seven half-hour talks given by other invited speakers. See all titles, abstracts, and schedule.