- Series
- Algebra Seminar
- Time
- Monday, November 14, 2022 - 1:30pm for 1 hour (actually 50 minutes)
- Location
- Clough 125 Classroom
- Speaker
- Sam Payne – The University of Texas, Austin – sampayne@utexas.edu – https://web.ma.utexas.edu/users/sampayne/
- Organizer
- Papri Dey
Cohomology groups of moduli spaces of curves are fruitfully studied from several mathematical perspectives, including geometric group theory, stably homotopy theory, and quantum algebra. Algebraic geometry endows these cohomology groups with additional structures (Hodge structures and Galois representations), and the Langlands program makes striking predictions about which such structures can appear. In this talk, I will present recent results inspired by, and in some cases surpassing, such predictions. These include the vanishing of odd cohomology on moduli spaces of stable curves in degrees less than 11, generators and relations for H^11, and new constructions of unstable cohomology on M_g.
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.