Title: Hodge theory of the moduli of vector bundles of degree 0.
Abstract: I will talk about some joint work with Dick Hain about the moduli space of rank n semistable bundles of degree 0 over a complex curve. As a topological space, this can be identified with the character variety of representations of the curve into GL(n) (or SL(n)), and cohomology of this space has a natural action by the mapping class group. When n=2, Cappell-Lee-Miller showed that the action of the Torelli subgroup on this is nontrivial. We found a partial generalization in higher rank. These results can be applied to study the mixed Hodge structure on the cohomology. In many cases, we can see that this is genuinely mixed (nonsplit).
