Colloquium abstracts

Vincent Pilloni
Ecole normale superieure de Lyon, France
February 28, 2019

On the Hasse-Weil conjecture:  Hasse and Weil conjectured that Zeta functions of varieties over numberfields admit meromorphic continuation and satisfy a functional equation. We will explain new results in the direction of this conjecture for genus 2 curves over totally real fields. The difficulty is that genus 2 curves have non-regular hodge numbers and the Taylor--Wiles method that was successful in proving the conjecture for genus 1 curves (for example) breaks down in several places. This is joint work with G. Boxer, F.Calegari and T. Gee.