4:00 pm Thursday, March 17, 2016

Kiran Kedlaya (UCSD)

Abstract: Consider a system of polynomial equations with integer coefficients. For
each prime number p, one can count the solutions of these equtaions in
the integers modulo p; while the structure of these counts is a rather
deep topic in number theory, one can pose statistical questions about
these counts for which the answers are expected to be somewhat simpler
(although still deep). We discuss several variations on this theme,
including the Chebotarev density theorem, the Sato-Tate conjecture for
elliptic curves, a general but imprecise conjecture of Serre, and a
precise form of Serre's conjecture for genus 2 curves due to
Fite-Kedlaya-Rotger-Sutherland.