Algebra and Geometry Seminar

I will discuss recent joint work with Madeline Brandt and Melody Chan, studying the weight zero compactly supported cohomology of the moduli space H_g,n of n-pointed hyperelliptic curves of genus g. We find a normal crossings compactification of this space using the theory of admissible G-covers, and then study the homology of the resulting dual complex using techniques from combinatorial topology. Our main result is a graph sum formula for the weight zero Euler characteristic, considered as a virtual representation of the symmetric group.