Jan McGarry Furriol: Homology of moduli spaces of manifolds

Abstract.

We will talk about an approach to understanding the homology of classifying spaces for bundles of manifolds due to Galatius and Randal-Williams, generalizing the solution of the Mumford conjecture by Madsen and Weiss. If time permits, we will mention how to use their results to calculate abelianizations of mapping class groups of generalized genus g surfaces or smooth hypersurfaces of four-dimensional complex projective space.