Old and new results in arithmetic statistics

Date: Thursday 11 August 2022

Abstract

Studying the statistical behavior of number theoretic quantities is presently in vogue. This lecture begins with a new look at classical results in number theory from the perspective of arithmetic statistics, and then turns to point counts for elliptic curves and K3 surfaces over finite fields. This lecture will use the celebrated Sato-Tate Conjecture (now theorem thanks to Richard Taylor and his collaborators) as motivation for refinements in several directions that arise from special properties of various types of q-series and hypergeometric functions. One of the results will feature the more exotic Batman distribution in the context of K3 surfaces.

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