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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

September 22, 2021 (12:15 PM PDT - 01:05 PM PDT)
Speaker(s): Emma Bailey (City University of New York (CUNY))
Location: MSRI: Simons Auditorium, Online/Virtual
Tags/Keywords
  • Characteristic polynomials

  • moments

  • l

  • t

  • Toeplitz determinant

  • symmetric function theory

  • Riemann zeta function

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Abstract

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.

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