Workshop on Additive Combinatorics and Algebraic Connections

Towards a Geometric Analogue of Sarnak's Conjecture

Abstract: Work of Mark Shusterman and myself has proven an analogue of Chowla's conjecture for polynomial rings over finite fields, which controls k-points correlations of the Möbius function for k bounded by a certain function of the finite field size. Sarnak has shown that Chowla's conjecture implies Sarnak's conjecture on correlations of the Möbius function with zero-entropy dynamical systems. However, our analogue is not quite strong enough to imply an analogue of Sarnak's conjecture, since that requires control on k-point correlations for all k. I will propose a geometric version of Sarnak's conjecture to which our methods do apply.

Date & Time

October 28, 2022 | 10:00am – 11:00am

Location

Simonyi 101 and Remote Access

Speakers

Will Sawin

Speaker Affiliation

Columbia University

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