Seminar series
Date
Tue, 13 Oct 2026
16:00
16:00
Location
L6
Speaker
George Snape
Organisation
University of Bristol
The joint moment problem asks to compute the averages of characteristic polynomials and their derivatives of random matrices drawn from one of the classical compact groups. Following the work of Bump and Gamburd (2006) and then Dehaye (2010), we will discuss the role of representation theory in this problem.
We then present recent work of the speaker giving an exact expression for these moments, valid for both finite matrix size and asymptotically. The expressions have a rich combinatorial structure, due to their relation to Kostka numbers and counting integer matrices (magic squares).
Time permitting, we will discuss a proof of a conjecture of Basor et al. (2018) on the connection between this problem and the irregular conformal block expansion of the Painlevé tau function.