# Heisenberg categorification and Hilbert Schemes

SPEAKER: Anthony Licata

TITLE: Heisenberg categorification and Hilbert Schemes

ABSTRACT: Associated to a finite subgroup of SL(2) there is an infinite dimensional Heisenberg algebra H and a complex surface X. Nakajima and Grojnowski constructed a representation of H a on the cohomology of Hilbert schemes of points on X. We give a diagrammatic categorification of the Heisenberg algebra, and construct an action of this categorification on the derived categories of Hilbert schemes. Passing to the Grothendieck group, this gives an action of a quantized Heisenberg algebra on the equivariant K-theory of Hilbert schemes. (Joint with Sabin Cautis)