Anthony Licata : Heisenberg algebras, Hilbert Schemes, and Graphical Categorifications

Posted by , part of the Algebraic Geometry Seminar.

At

Dec. 2, 2010, 4 p.m.

In

SEO 636

Abstract

For every finite subgroup G of SU(2) there is an associated infinite dimensional Heisenberg algebra. Nakajima and Grojnowski constructed representations of these Heisenberg algebras on the cohomology of Hilbert schemes of points on the corresponding ALE space. We give a graphical categorification of the Heisenberg algebra, and prove that this categorification acts on the derived categories of Hilbert schemes. This is joint work with Sabin Cautis.