George Snape

A representation theoretic approach to the CUE joint moment problem

The joint moment problem concerns the computation of averages of characteristic polynomials and their derivatives for random matrices drawn from the classical compact groups. In this talk, we discuss the motivation behind this problem from both a random matrix theory and number-theoretic perspective.

We then present recent work of the speaker giving an exact expression for these moments, valid for both finite matrix size and asymptotically, via an extension of Dehaye's representation-theoretic approach. Time permitting, we will discuss a proof of a conjecture of Basor, Bleher, Buckingham, Grava, Its, Its, and Keating on the connection between this problem and the conformal block expansion of the Painlevé tau function.