Colloquium - Jose Simental Rodriguez

Date: February 7, 2022

Time: 2:00PM - 3:00PM

Location: ZOOM

Speaker: Jose Simental Rodriquez, Max-Planck-Intitut fur Mathematik

Description:
Title: Catalan combinatorics, Quantized Gieseker varieties and homology of torus knots
Abstract: In the past decade the aims and techniques of classical representation theory have been greatly generalized to study representations of quantizations of symplectic singularities. In this talk, I will focus on one example that already exhibits many of the interesting parts of the theory, these are the quantized Gieseker varieties from the title. I will tie their finite-dimensional representation theory to classical Catalan combinatorics and elaborate on how these finite-dimensional representations conjecturally give the Khovanov-Rozansky homology of torus knots, a powerful invariant that is notoriously difficult to compute. Time permitting I will also give connections to the geometry of Hilbert schemes on singular curves, and give some directions of future research.