Tuesday, February 14th, 2017
12:30pm - 1:30pm, in McCormack 2-207

Anton Mellit

IST, Austria

Cohomology of character varieties

Abstract: Character varieties are spaces that parametrize representations of fundamental groups of Riemann surfaces with punctures, with prescribed local monodromies around the punctures. Via Simpson's correspondence, they are diffeomorphic to moduli spaces of semistable Higgs bundles. A recent conjecture of Hausel, Letellier and Rodriguez-Villegas gives an explicit formula for the Betti numbers of these spaces, relating them to Hilbert schemes. In another development Gorsky, Oblomkov, Rasmussen and Shende conjectured an explicit connection between Hilbert schemes and certain invariants of torus knots and links. In this talk I will explain the main objects of these stories, how they are connected, and, if time permits, my results in this area.