GAAG seminar - Character stacks and varieties for Riemann surfaces

Given a punctured Riemann surface X, character stacks and varieties are geometric objects which parametrize  local systems on X with prescribed local monodromies. 

The cohomology of character stacks and varieties is almost completely understood in the case of a generic choice of monodromies, thanks to the work of Hausel, Letellier and Rodriguez-Villegas and Mellit. Much less is known about the non-generic case.

 In the first part of the talk, I will introduce and define character stacks and varieties and review the known results about the cohomology of these objects. In the second part, I will focus on the non-generic case and give a sketch of the proof of a formula for the E-series of non-generic character stacks, which is the main result of my PhD thesis.