Todd Kemp (UCSD)
Title: Random Matrices, Heat Flow, and Lie Groups
Abstract: Random matrix theory studies the behavior of the eigenvalues and eigenvectors of random matrices as the dimension grows. In the age of data science, it has become one of the hottest fields in probability theory and many parts of applied science, from material deposition to wireless communication. Initiated by Wigner in the 1950s (with some key results going back further to Wishart and other statisticians in the 1920s), there is now a rich and well-developed theory of the universal behavior of random spectral statistics in models that are natural generalizations of the Gaussian case.
In this talk, I will discuss a generalization of these kinds of results in a new direction. A Gaussian random matrix can be thought of as an instance of Brownian motion on a Lie algebra; this opens the door to studying the eigenvalues of Brownian motion on Lie groups. I will present recent progress understanding the asymptotic spectral distribution of Brownian motion on unitary groups and general linear groups. The tools needed include probability theory, functional analysis, combinatorics, and representation theory. No technical background is required; only an interest in trying to understand some cool and mysterious pictures.
Friday, April 27, 2018 at 3:30pm to 4:30pm
Levan Center, 201
2322 N Kenmore Ave