Rice University Department of Mathematics Colloquium

Equidistribution of Frobenius eigenvalues

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.

Return to Colloquium page