Twisted moduli spaces and Duistermaat-Heckman measures
In our terminology, a twisted moduli space is a character variety parametrizing a certain class of local systems on a bordered surface, where the transition functions are allowed to take values in a non-connected Lie group. Such spaces give a natural generalization of moduli of flat G-bundles, and are endowed with a so-called "twisted" quasi-Hamiltonian structure.
The purpose of this talk is to give an accessible introduction to the topics of the previous paragraph. Time permitting, we will discuss an important symplectic invariant of twisted moduli spaces, their Duistermaat-Heckman measure, which is a group-valued generalization of the eponymous measure in symplectic geometry.