Departmental Colloquium
Todd Kemp
University of California San Diego
Random Matrices, Heat Flow, and Lie Groups
Abstract: Random matrix theory studies the behavior of the eigenvalues (or singular values)
of random matrices as the dimension grows. Initiated by Wigner in the 1950s,
there is now a rich and well-developed theory of the universal behavior of such
random eigenvalues 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 (and
singular values) 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, combinatorics, and representation theory.
Tea at 4:15 SEO 300
Friday September 23, 2016 at 3:00 PM in SEO 636