Abstract: This talk will discuss two closely-related geometric questions about the moduli space of vector bundles on an algebraic curve and its cotangent bundle, the moduli space of Higgs bundles. One involves computing some intersection-theoretic invariants of the nilpotent cone and the other involves understanding the stalks of the Hecke eigensheaves on this moduli space defined in the geometric Langlands program. The motivation for these problems comes from classical number theory and the relationship between the two passes through a new characteristic p version of a general theorem of Massey. The talk will give an overview of all these aspects.

Zoom link: https://yale.zoom.us/j/99305994163, contact the organizers (Gurbir Dhillon and Junliang Shen) for the passcode.