June 15: Anton Mellit

Title: Counting bundles and Macdonald polynomials

Abstract:

Many interesting functions arise as generating functions of geometric invariants. There are different kinds of invariants one can consider, such as Euler characteristics of spaces or holomorphic vector bundles or their equivariant generalizations. I will talk about another way to produce invariants: counting points over finite fields. I will explain how the Hall-Littlewood polynomials (both modified and unmodified) can be obtained this way. Then I will explain how to obtainMacdonald polynomials and generating functions considered by Hausel, Letellier and Rodriguez-Villegas (a type of Nekrasov partition functions) by counting bundles with endomorphisms or twisted endomorphisms.