Seminars and Colloquia by Series

An elementary proof of the A2 bound

Series
Analysis Seminar
Time
Wednesday, January 21, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Michael Lacey – Georgia Tech
The sharp A2 weighted bound for martingale transforms can be proved by a new elementary method. With additional work, it can be extended to the euclidean setting. Other generalizations should be possible.

The Cartan-Hadamard Problem and the Little Prince

Series
Geometry Topology Seminar
Time
Tuesday, January 20, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Greg Kuperberg – UCDavis –
Among n-dimensional regions with fixed volume, which one hasthe least boundary? This question is known as an isoperimetricproblem; its nature depends on what is meant by a "region". I willdiscuss variations of an isoperimetric problem known as thegeneralized Cartan-Hadamard conjecture: If Ω is a region in acomplete, simply connected n-manifold with curvature bounded above byκ ≤ 0, then does it have the least boundary when the curvature equalsκ and Ω is round? This conjecture was proven when n = 2 by Weil andBol; when n = 3 by Kleiner, and when n = 4 and κ = 0 by Croke. Injoint work with Benoit Kloeckner, we generalize Croke's result to mostof the case κ < 0, and we establish a theorem for κ > 0. It was originally inspired by the problem of finding the optimal shape of aplanet to maximize gravity at a single point, such as the place wherethe Little Prince stands on his own small planet.

Binary linear codes via 4D discrete Ihara-Selberg function

Series
Graph Theory Seminar
Time
Tuesday, January 20, 2015 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Martin Loebl – Charles University
We express weight enumerator of each binary linear code as a product. An analogous result was obtain by R. Feynman in the beginning of 60's for the speacial case of the cycle space of the planar graphs.

Random polytopes and estimation of convex bodies

Series
Job Candidate Talk
Time
Tuesday, January 20, 2015 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Victor-Emmanuel Brunel – Yale University
In this talk we will discuss properties of some random polytopes. In particular, we first propose a deviation inequality for the convex hull of i.i.d. random points, uniformly distributed in a convex body. We then discuss statistical properties of this random polytope, in particular, its optimality, when one aims to estimate the support of the corresponding uniform distribution, if it is unknown.We also define a notion of multidimensional quantiles, related to the convex floating bodies, or Tukey depth level sets, for probability measures in a Euclidean space. When i.i.d. random points are available, these multidimensional quantiles can be estimated using their empirical version, similarly to the one-dimensional case, where order statistics estimate the usual quantiles.

Stability of Matter

Series
PDE Working Seminar
Time
Friday, January 16, 2015 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 202
Speaker
Michael Loss – GeorgiaTech –
It is an everyday observation that the internal energy of a piece of material is extensive, i.e., proportional to the number of atoms in this material. A celebrated result of Dyson and Lenard (1967) explains this fact on the basis of quantum mechanics, the fundamental theory that is the basis for the description of the material world. The proof of Dyson and Lenard was greatly simplified by Lieb and Thirring (1975) using Thomas Fermi theory and what is now called the Lieb-Thirring inequality. In these talks I explain the notion of Stability, give an outline of the Lieb-Thirring proof and explain a proof of the Lieb-Thirring inequality with good constants. If time permits I will talk about further developments, like systems interacting with magnetic fields.

Pursuit on a Graph

Series
ACO Student Seminar
Time
Friday, January 16, 2015 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Peter Winkler – Dartmouth College

Please Note: Joint ARC colloquium/ACO student seminar

Pursuit games---motivated historically by military tactics---are a natural for graphical settings, and take many forms. We will present some recent results involving (among other things) drunks, Kakeya sets and a "ketchup graph.'' Lastly, we describe what we think is the most important open problem in the field.

First Meeting

Series
Convex Algebraic Geometry Reading Seminar
Time
Friday, January 16, 2015 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Greg Blekherman – Georgia Tech
The topic this semester will be Nonnegative and PSD Ranks of matrices. We will begin by discussing the article "Lifts of Convex Sets and Cone Factorizations" by Gouveia, Parrilo and Thomas, which makes the connection between factoring slack matrices of polytopes and finding computationally efficient representations of polytopes.

Interlacing families: a new technique for controlling eigenvalues

Series
Job Candidate Talk
Time
Thursday, January 15, 2015 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles006
Speaker
Adam Marcus – Yale University
Matrices are one of the most fundamental structures in mathematics, and it is well known that the behavior of a matrix is dictated by its eigenvalues. Eigenvalues, however, are notoriously hard to control, due in part to the lack of techniques available. In this talk, I will present a new technique that we call the "method of interlacing polynomials" which has been used recently to give unprecedented bounds on eigenvalues, and as a result, new insight into a number of old problems. I will discuss some of these recent breakthroughs, which include the existence of Ramanujan graphs of all degrees, a resolution to the famous Kadison-Singer problem, and most recently an incredible result of Anari and Gharan that has led to an interesting new anomaly in computer science. This talk will be directed at a general mathematics audience and represents joint work with Dan Spielman and Nikhil Srivastava.

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