Forthcoming events in this series


Wed, 15 Jun 2011

11:00 - 12:00
Gibson 1st Floor SR

Wigner-Dyson conjecture on random matrices and Erdos-Renyi graphs

Horng-Tzer Yau
(Harvard, USA)
Abstract

Random matrices were introduced by E. Wigner to model the excitation spectrum of large nuclei. The central idea is based on the hypothesis that the local statistics of the excitation spectrum for a large complicated system is universal. Dyson Brownian motion is the flow of eigenvalues of random matrices when each matrix element performs independent Brownian motions. In this lecture, we will explain the connection between the universality of random matrices and the approach to local equilibrium of Dyson Brownian motion. The main tools in our approach are the logarithmic Sobolev inequality and entropy flow. The method will be applied to the adjacency matrices of Erdos-Renyi graphs.

Tue, 14 Jun 2011

12:30 - 13:30
Gibson 1st Floor SR

Entropy and isometric embedding

Marshall Slemrod
(University of Wisconsin)
Abstract

The problem of isometric embedding of a Riemannian Manifold into

Euclidean space is a classical issue in differential geometry and

nonlinear PDE. In this talk, I will outline recent work my

co-workers and I have done, using ideas from continuum mechanics as a guide,

formulating the problem, and giving (we hope) some new insight

into the role of " entropy".