Erik Carlsson, Harvard University
Title: Hilbert schemes, combinatorics, and character varieties
Abstract: I'll explain the remarkable connections between the algebraic combinatorics that appear in the Hilbert scheme of points, and character varieties, as predicted by the conjectures of Hausel, Letellier, and Rodriguez-Villegas. I'll then discuss some recent results and potential future directions in these areas with Rodriguez-Villegas and Mellit. Interestingly, one of the objects that appears is the K-theoretic Ext^1 operator
studied by Nekrasov, Okounkov and myself, that appears in the AGT conjectures in higher rank.
