April 8: Will Sawin

Title: The polar multiplicities of the nilpotent cone in the module space of Higgs bundles

Abstract: The polar multiplicities are some intersection-theoretic invariants associated to a conical cycle in the cotangent bundle of a variety and a point on that variety. Motivated by a problem in number theory, we aim to compute these for the nilpotent cone in the moduli space of Higgs bundles. We begin to answer this by handling the first nontrivial case (rank 2, genus 0, with level structure).