**Geometry and Topology Weekly Seminar**

Mixed Hodge Structures of Character Varieties

Azizeh Nozad, IPM

14 JUN 2023

15:30 - 17:00

The topology of character varieties of surface groups is well known to be of fundamental importance, in part through its relationship, via the non-abelian Hodge theory to the moduli spaces of Higgs bundles. The calculation of Serre (also known as E-) polynomials of these varieties received an important impetus with works of Hausel and Rodriguez-Villegas (2008). These arithmetic methods, as well as new geometric techniques have been successfully developed and applied to other cases, like moduli of quiver representations, and character varieties of free or free abelian groups. In this talk we will introduce another point of view in the computations of the E-polynomials of character varieties for arbitrary finitely presented groups, based on a natural stratification coming from affine GIT and the combinatorics of partitions.