Algebraic Combinatorics Seminar - Jonathan Novak

Title: A tale of two integrals

Abstract:

The Harish-Chandra/Itzykson-Zuber (HCIZ) and Brezin-Gross-Witten (BGW) integrals are a pair matrix integrals which play a prominent role in quantum field theory. Remarkably, these ubiquitous special functions are also significant from the perspective of algebraic combinatorics: they are generating functions for certain classes of Hurwitz numbers. I will explain the connection between the HCIZ/BGW integrals and Hurwitz theory, and explain how it leads to a proof of some old conjectures concerning the asymptotic behavior of these integrals. This is based in part on joint work with Ian Goulden and Mathieu Guay-Paquet.