Differential Geometry Seminar: Geometry of character varieties

Speaker: Stefano Giannini

 

Title: Geometry of character varieties

 

Abstract: Character varieties associated to surface groups have deep connections to various fields of mathematics and physics, for instance through the non-abelian Hodge correspondence. I will begin by introducing these spaces together with their additive analogues. Then I will explain how arithmetic methods—specifically, point-counting over finite fields—can be used to study the cohomology of these spaces, and I will present some recent results in this direction.