Questions about the geometry of G-representation varieties on a manifold M have attracted many researchers as the theory combines the algebraic geometry of G, the topology of M, and the group theory and representation theory of G and the fundamental group of M. In this talk, I will explain how to construct a Topological Quantum Field Theory to compute virtual classes of character stacks (G-representation varieties equipped with the adjoint G-action) in the Grothendieck ring of stacks. I will also show a few features of the construction (for instance, how to obtain arithmetic information) focusing on a couple of simple examples.
The work is joint with Jesse Vogel and Ángel González-Prieto.
