Generalized Moments of the Classical Compact Groups
[HYBRID WORKSHOP] Connections and Introductory Workshop: Universality and Integrability in Random Matrix Theory and Interacting Particle Systems, Part 2 September 20, 2021 - September 24, 2021
Location: MSRI: Simons Auditorium, Online/Virtual
symmetric function theory
Riemann zeta function
This talk will cover a natural generalization of moments of characteristic polynomials from the classical compact groups (unitary, symplectic, orthogonal). The results presented resolve a conjecture of Fyodorov and Keating. There are natural connections to log-correlated fields, integrable systems (asymptotics of Toeplitz and Hankel determinants, Painlevé), symmetric function theory, and number theory.