# Mathematics Colloquia and Seminars

### The trace of the quantum Heisenberg category

Algebra & Discrete Mathematics

 Speaker: Peter Samuelson, U Edinburgh Related Webpage: http://www.maths.ed.ac.uk/~psamuels/ Location: 2112 MSB Start time: Mon, Jan 9 2017, 4:10PM

Khovanov and Licata-Savage (for q=1 and generic q, respectively) introduced a

diagramatically defined monoidal category whose K-theory is the Heisenberg

algebra. They also defined a "2-representation" of this category, where (1)

objects are sent to compositions of induction and restriction functors for

Hecke algebras, (2) morphisms are sent to certain natural transformations

between these functors, and (3) the tensor product is sent to functor

composition. We give an algebra presentation of the trace (or Hochschild

homology) of this category and show it is isomorphic to a central extension

of the elliptic Hall algebra of Burban and Schiffmann, which is the

"universal" Hall algebra of an elliptic curve. (This is joint work with

Cautis, Lauda, Licata, and Sussan.)

Peter will be visiting M-W.