Abstract: The Heisenberg algebra plays a vital role in many areas of mathematics and physics. In this talk, we will discuss a general method for categorifying this algebra. That is, we introduce a family of categories, depending on a Frobenius superalgebra B, whose Grothendieck groups are isomorphic to the Heisenberg algebra. The categories are graphical in nature, consisting of planar diagrams modulo local relations, and they act naturally on the category of finitely generated projective modules over wreath product algebras corresponding to B. Appropriate specializations of B recover results of Khovanov and Cautis-Licata. This is joint work with Daniele Rosso.
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