Videos

Towards a Geometric Analogue of Sarnak's Conjecture

Presenter
October 28, 2022
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.