Thomas Wennink: Weight graded pieces of the cohomology of moduli spaces of pointed smooth curves

Abstract:

This is a report of joint work with Jonas Bergström. We have written a computer program that implements Deligne's weight spectral sequence and the Getzler–Kapranov complex, to compute the weight graded pieces of cohomology of moduli spaces of pointed smooth curves. This can be applied for concrete computations for small g and n: namely, in cases where the cohomology groups appearing in the boundary stratification of the Deligne–Mumford compactification are generated by tautological classes (and when Pixton's relations are all relations). In particular we calculated the cohomology and Hodge numbers of M₅ and M_3,3, which were not known before.