Title: Cohomology of moduli spaces of curves
Speaker: Sam Payne
Speaker Info: UT Austin
The cohomology groups of moduli spaces of curves are important to several mathematical disciplines, from low-dimensional topology and geometric group theory to stable homotopy theory and mathematical physics. Algebraic geometry endows these groups with additional structures, such as Hodge structures and Galois representations, and the Langlands program makes striking predictions about which such structures can appear. In this talk, I will survey recent results confirming several of these predictions and using the Hodge structures and Galois representations on the cohomology groups of moduli spaces to make progress on questions of basic interest, such as:Date: Wednesday, October 12, 2022
For which g and k is H^k(M_g) nonzero?
Based on joint work with Jonas Bergström and Carel Faber; with Sam Canning and Hannah Larson; with Melody Chan and Søren Galatius; and with Thomas Willwacher.