Seminars and Colloquia by Series

Hypergraph Ramsey Problems

Series
Combinatorics Seminar
Time
Friday, April 5, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dhruv Mubayi – University of Illinois, Chicago
I will survey the major results in graph and hypergraph Ramsey theory and present some recent results on hypergraph Ramsey numbers. This includes a hypergraph generalization of the graph Ramsey number R(3,t) proved recently with Kostochka and Verstraete. If time permits some proofs will be presented.

Integral homology of hyperbolic three--manifolds

Series
Geometry Topology Seminar
Time
Friday, April 5, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jean Raimbault – Institut de Mathematiques de Jussieu, Universite Pierre et Marie Curie
It is a natural question to ask whether one can deduce topological properties of a finite--volume three--manifold from its Riemannian invariants such as volume and systole. In all generality this is impossible, for example a given manifold has sequences of finite covers with either linear or sub-linear growth. However under a geometric assumption, which is satisfied for example by some naturally defined sequences of arithmetic manifolds, one can prove results on the asymptotics of the first integral homology. I will try to explain these results in the compact case (this is part of a joint work with M. Abert, N. Bergeron, I. Biringer, T. Gelander, N. Nikolov and I. Samet) and time permitting I will discuss their extension to manifolds with cusps such as hyperbolic knot complements.

Tutorial: Information-based complexity of convex optimization

Series
ACO Student Seminar
Time
Friday, April 5, 2013 - 13:05 for 1 hour (actually 50 minutes)
Location
ISyE Executive classroom
Speaker
Cristobal Guzman – ISyE, Georgia Tech –
Information-based complexity is an alternative to Turing complexity that is well-suited for understanding a broad class of convex optimization algorithms. The groundbreaking work of Nemirovski and Yudin provided the basis of the theory, establishing tight lower bounds on the running time of first-order methods in a number of settings. There has been a recent interest on these classical techniques, because of exciting new applications on Machine Learning, Signal Processing, Stochastic Programming, among others. In this talk, we will introduce the rudiments of the theory, some examples, and open problems. Based on joint work with Gábor Braun and Sebastian Pokutta.

Conormals and contact homology VIII

Series
Geometry Topology Working Seminar
Time
Friday, April 5, 2013 - 11:30 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
John Etnyre – Georgia Tech
In this series of talks I will begin by discussing the idea of studying smooth manifolds and their submanifolds using the symplectic (and contact) geometry of their cotangent bundles. I will then discuss Legendrian contact homology, a powerful invariant of Legendrian submanifolds of contact manifolds. After discussing the theory of contact homology, examples and useful computational techniques, I will combine this with the conormal discussion to define Knot Contact Homology and discuss its many wonders properties and conjectures concerning its connection to other invariants of knots in S^3.

On Adam Jakubowski's approach to proving asymptotic results for regularly varying sequences

Series
Stochastics Seminar
Time
Thursday, April 4, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Thomas Mikosch – University of Copenhagen
In recent work, an idea of Adam Jakubowski was used to prove infinite stable limit theory and precise large deviation results for sums of strictly stationary regularly varying sequences. The idea of Jakubowski consists of approximating tail probabilities of distributions for such sums with increasing index by the corresponding quantities for sums with fixed index. This idea can also be made to work for Laplace functionals of point processes, the distribution function of maxima and the characteristic functions of partial sums of stationary sequences. In each of these situations, extremal dependence manifests in the appearance of suitable cluster indices (extremal index for maxima, cluster index for sums,...). The proposed method can be easily understood and has the potential to function as heuristics for proving limit results for weakly dependent heavy-tailed sequences.

Quasirandom Hypergraphs

Series
Graph Theory Seminar
Time
Thursday, April 4, 2013 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dhruv Mubayi – University of Illinois at Chicago
Since the foundational results of Thomason and Chung-Graham-Wilson on quasirandom graphs over 20 years ago, there has been a lot of effort by many researchers to extend the theory to hypergraphs. I will present some of this history, and then describe our recent results that provide such a generalization and unify much of the previous work. One key new aspect in the theory is a systematic study of hypergraph eigenvalues first introduced by Friedman and Wigderson. This is joint work with John Lenz.

CANCELLED: Minimal Energy and Maximal Polarization

Series
School of Mathematics Colloquium
Time
Thursday, April 4, 2013 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ed Saff – Vanderbilt University
While this could be a lecture about our US Congress, it instead deals with problems that are asymptotically related to best-packing and best-covering. In particular, we discuss how to efficiently generate N points on a d-dimensional manifold that have the desirable qualities of well-separation and optimal order covering radius, while asymptotically having a prescribed distribution. Even for certain small numbers of points like N=5, optimal arrangements with regard to energy and polarization can be a challenging problem.

Operator theory from several complex variables perspective

Series
Analysis Seminar
Time
Wednesday, April 3, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Sonmez Sahutoglu – University of Toledo
Complex analysis in several variables is very different from the one variable theory. Hence it is natural to expect that operator theory on Bergman spaces of pseudoconvex domains in $\mathbb{C}^n$ will be different from the one on the Bergman space on the unit disk. In this talk I will present several results that highlight this difference about compactness of Hankel operators. This is joint work with Mehmet Celik and Zeljko Cuckovic.

The Stability of the dust-Einstein System with a Positive Cosmological Constant

Series
PDE Seminar
Time
Tuesday, April 2, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Mahir Hadzic – MIT
We study small perturbations of the well-known Friedman-Lemaitre-Robertson-Walker (FLRW) solutions to the dust-Einstein system with a positive cosmological constant on a spatially periodic background. These solutions model a quiet fluid in a spacetime undergoing accelerated expansion. We show that the FLRW solutions are nonlinearly globally future-stable under small perturbations of their initial data. Our result extends the stability results of Rodnianski and Speck for the Euler-Einstein system with positive cosmological constant to the case of dust (i.e. a pressureless fluid). The main difficulty that we overcome is the degenerate nature of the dust model that loses one degree of differentiability with respect to the Euler case. To resolve it, we commute the equations with a well-chosen differential operator and develop a new family of elliptic estimates that complement the energy estimates. This is joint work with J. Speck.

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