A conjecture of Hausel on the cohomology of moduli spaces of Higgs bundles (Jochen Heinloth)
by Jochen Heinloth (Essen)
The moduli spaces of Higgs bundles on a curve contains a very rich geometric structure. For example, considered as a manifold, it admits different algebraic structures which have very different properties: For one structure one can give explicit equations, but it is hard to understand the geometry - in the other one has a lot of geometric structure, but to give equations would be difficult. These two points of view, led to a series of results and conjectures on the structure of the cohomology of these spaces. In the first part of my talk, I will try to explain the basic results on these spaces and explain a naive approach to describe the spaces by a cut and paste method.
In the second part I want to explain how one can prove a conjecture of Hausel on a particular cohomological invariant (the y-genus) of the moduli spaces using these methods. This is joint work with O. Garcia-Prada and A. Schmitt.