# Topological Quantum Field Theory Seminar

### A diagrammatic categorification of the higher level Heisenberg algebras

Khovanov defined a diagrammatic 2-category and conjectured (and partially proved) that it categorifies the level-one Heisenberg algebra. Since then, several interesting generalizations and applications have been found, e.g. Cautis and Licata's generalization involving Hilbert schemes and their construction of categorical vertex operators. However, these are all for level one. In my talk, I will explain Alistair Savage and my results on a generalization of Khovanov's original results for higher level Heisenberg algebras. This is work in progress.