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The Fyodorov-Hiary-Keating Conjecture

[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 24, 2021 (09:00 AM PDT - 09:50 AM PDT)
Speaker(s): Paul Bourgade (New York University, Courant Institute)
Location: MSRI: Simons Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
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Abstract

Fyodorov-Hiary-Keating proposed very precise asymptotics for the maximum of the Riemann zeta function in almost all intervals along the critical axis. After reviewing the origins of this conjecture through the random matrix analogy, I will explain a proof up to tightness, building on an underlying branching structure. This work with Louis-Pierre Arguin and Maksym Radziwill relies on a multiscale analysis and twisted moments of zeta.

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