Graduate Student / Postdoc Seminar

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Random matrices, quantum chaos and analytic number theory

Speaker: Paul Bourgade, Courant (NYU)

Location: Warren Weaver Hall 1302

Date: Friday, December 10, 2021, 11:15 a.m.

Synopsis:

Abstract: This lecture will review the mostly conjectural occurrence of random matrix statistics in deterministic settings, such as the behavior of the Riemann zeta function on the critical line or the spectral properties of the Laplacian on generic manifolds. I will explain the contributions of Selberg on the central limit theorem for zeta, Montgomery on the pair correlation of the critical zeros, Bohigas-Giannoni-Schmit on quantum chaos, and Fyodorov-Hiary-Keating for the local extrema of the Riemann zeta function.