Jonathan Novak, UC San Diego  

Title: Hypergeometric functions of huge matrices

Abstract: Hypergeometric functions of complex matrices were introduced by James in the 1960s, building on work of Bochner and Herz. These remarkable multivariate generalizations of classical hypergeometric functions play a  fundamental role in the spectral analysis of random matrices, and a longstanding problem is to approximate them in the high-dimensional regime. I'll explain an algebraic combinatorics approach to this problem which uses symmetric functions and representation theory to effectively get around some hard apparently very difficult analysis.