Apr 2, 2020

Hilbert schemes of points on singular surfaces: combinatorics, geometry, and representation theory

Date: April 2, 2020 | 2:00 pm – 4:00 pm
Speaker: Balazs Szendroi , University of Oxford
Location: https://zoom.us/j/626437329

Given a smooth algebraic surface S over the complex numbers, the Hilbert scheme of points of S is the starting point for many investigations, leading in particular to generating functions with modular behaviour and Heisenberg algebra representations. I will explain aspects of a similar story for surfaces with rational double points, with links to algebraic combinatorics and the representation theory of affine Lie algebras. I will in particular explain our 2015 conjecture concerning the generating function of their Euler characteristics, and aspects of more recent work that lead to a very recent proof of the conjecture by Nakajima. Joint work with Gyenge and Nemethi, respectively Craw, Gammelgaard and Gyenge.