Title: Polynomial point counts and odd cohomology vanishing on moduli spaces of stable curves
Speaker: Sam Payne
Speaker Info: University of Texas at Austin
I will present two new results about point counting over finite fields and rational cohomology of moduli spaces of curves. The first says that the number of F_q-points on the moduli space of curves of genus 4 with n marked points, for n at most 3, is a polynomial in q. The second, which relies on the first, says that the rational singular cohomology of the moduli space of stable curves of genus g with n marked points vanishes in all odd degrees less than 11, for all g and n. Both results confirm predictions of the Langlands program, via the conjectural correspondence with polarized algebraic cuspidal automorphic representations of conductor 1, which have been classified in low weight by Chenevier and Lannes. The vanishing result for odd cohomology answers a question posed by Arbarello and Cornalba in the 1990s, and the bound of 11 is sharp.Date: Wednesday, October 12, 2022
Based on joint work with Jonas Bergström and Carel Faber.