Cohomology of moduli spaces

Cohomology of moduli spaces

Thu, 03/06/2010
12:00 		Oscar Randal-Williams (Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
Cohomology of moduli spaces
I will discuss what is known about the cohomology of several moduli spaces coming from algebraic and differential geometry. These are: moduli spaces of non-singular curves (= Riemann surfaces) $ M_g $, moduli spaces of nodal curves $ \overline{M}_g $, moduli spaces of holomorphic line bundles on curves $ Hol_g^k \to M_g $, and the universal Picard varieties $ Pic^k_g \to M_g $. I will construct characteristic classes on these spaces, talk about their homological stability, and try to explain why the constructed classes are the only stable ones. If there is time I will also talk about the Picard groups of these moduli spaces. Much of this work is due to other people, but some is joint with J. Ebert.