Seminars and Colloquia by Series

The van der Waerden Number and Colorings of Hypergraphs

Series
Combinatorics Seminar
Time
Friday, November 16, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dmitry Shabanov – Moscow State University and Yandex Corporate
The talk is devoted to the classical problem of estimating the Van der Waerden number W(n,k). The famous Van der Waerden theorem states that, for any integers n\ge 3, k\ge 2, there exists the smallest integer W(n,k) such that in any k-coloring of the set {1,2,...,W(n,k)}, there exists a monochromatic arithmetic progression of length n. Our talk is focused on the lower bounds for the van der Waerden number. We shall show that estimating W(n,k) from below is closely connected with extremal problems concerning colorings of uniform hypergraphs with large girth. We present a new lower bound for W(n,k), whose proof is based on a continuous-time random recoloring process.

On linear programming formulations of the TSP polytope

Series
ACO Student Seminar
Time
Friday, November 16, 2012 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Sebastian Pokutta – Georgia Tech, ISyE
We solve a 20-year old problem posed by M. Yannakakis and prove that there exists no polynomial-size linear program (LP) whose associated polytope projects to the traveling salesman polytope, even if the LP is not required to be symmetric. Moreover, we prove that this holds also for the maximum cut problem and the stable set problem. These results follow from a new connection that we make between one-way quantum communication protocols and semidefinite programming reformulations of LPs. (joint work with Samuel Fiorini, Serge Massar, Hans Raj Tiwary, and Ronald de Wolf)

A new twist on the Carleson operator

Series
Job Candidate Talk
Time
Thursday, November 15, 2012 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Lillian Pierce – University of Oxford –
Must the Fourier series of an L^2 function converge pointwise almost everywhere? In the 1960's, Carleson answered this question in the affirmative, by studying a particular type of maximal singular integral operator, which has since become known as the Carleson operator. In the past 40 years, a number of important results have been proved for generalizations of the original Carleson operator. In this talk we will describe new joint work with Po Lam Yung that introduces curved structure to the setting of Carleson operators.

Calibrated Elastic Regularization in Matrix Completion

Series
Stochastics Seminar
Time
Thursday, November 15, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skyles 006
Speaker
Cun-Hui Zhang – Rutgers University
This paper concerns the problem of matrix completion, which is to estimate a matrix from observations in a small subset of indices. We propose a calibrated spectrum elastic net method with a sum of the nuclear and Frobenius penalties and develop an iterative algorithm to solve the convex minimization problem. The iterative algorithm alternates between imputing the missing entries in the incomplete matrix by the current guess and estimating the matrix by a scaled soft-thresholding singular value decomposition of the imputed matrix until the resulting matrix converges. A calibration step follows to correct the bias caused by the Frobenius penalty. Under proper coherence conditions and for suitable penalties levels, we prove that the proposed estimator achieves an error bound of nearly optimal order and in proportion to the noise level. This provides a unified analysis of the noisy and noiseless matrix completion problems. Tingni Sun and Cun-Hui Zhang, Rutgers University

Divisors on graphs and connected flags

Series
Graph Theory Seminar
Time
Thursday, November 15, 2012 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Farbod Shokrieh – Math, GT
Associated to every finite graph G there is a canonical ideal which encodes the linear equivalences of divisors on G. In the study of this ideal the concept of "connected flags" arise naturally. The focus of this talk will be the study of combinatorial properties of these connected flags. This is a joint work with Fatemeh Mohammadi. (This talk is related to the talk I gave on October 12th in the Combinatorics seminar, but I will not assume anything from the previous talk.)

Braid Groups and Hodge Theory

Series
Geometry Topology Student Seminar
Time
Wednesday, November 14, 2012 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Becca Winarski – Georgia Tech
We look at a paper of McMullen "Braid Groups and Hodge Theory" exploring representations of braid groups and their connections to arithemetic lattices.

From a formula of Haagerup to random matrices and free probability

Series
Analysis Seminar
Time
Wednesday, November 14, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ionel Popescu – Georgia Tech –
This formula of Haagerup gives an expression of the log|x-y| in terms of Chebyshev polynomials of the first kind. This is very useful for problems involving the logarithmic potentials which plays a prominent role in random matrices, free probability, orthogonal polynomials and other areas. We will show how one can go from this to several things, for example the counting problems of planar diagrams and functional inequalities in free probability in particular an intriguing Poincare inequality and some related other inequalities. If time allows I will also talk about a conjecture related to the Hilbert transform, semicircular and arcsine distribution. Parts of this was with Stavros Garoufalidis and some other parts with Michel Ledoux.

Diophantine equations and p-adic analysis

Series
Research Horizons Seminar
Time
Wednesday, November 14, 2012 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Matt Baker – Georgia Tech, School of Math
I will discuss how one can solve certain concrete problems in number theory, for example the Diophantine equation 2x^2 + 1 = 3^m, using p-adic analysis. No previous knowledge of p-adic numbers will be assumed. If time permits, I will discuss how similar p-adic analytic methods can be used to prove the famous Skolem-Mahler-Lech theorem: If a_n is a sequence of complex numbers satisfying some finite-order linear recurrence, then for any complex number b there are only finitely many n for which a_n = b.

Regularity of the flow map for the gravity-capillary problem

Series
PDE Seminar
Time
Tuesday, November 13, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ming Chen – University of Pittsburgh
We prove via explicitly constructed initial data that solutionsto the gravity-capillary wave system in R^3 representing a 2d air-waterinterface immediately fail to be C^3 with respect to the initial data ifthe initial (h_0, \psi_0) \in H^{s + 1/2} \times H^s for s<3, where h isthe free surface and \psi is the velocity potential.

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