Title: The Heisenberg category of a category, Speaker(s): Ádám Gyenge, Alfréd Rényi Institute of Mathematics, Date and time: 19 Oct 2022, 15:00 (Europe/Rome), Lecture series: Algebraic and Arithmetic Geometry Seminar, Venue: Department of Mathematics (Aula Magna).

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Abstract --------

The Heisenberg algebra associated with a lattice is a much-investigated object originating in quantum theory. Khovanov introducedrecently a categorification of the infinite Heisenberg algebraassociated with the free boson or, equivalently, a rank 1 lattice,using a graphical construction involving planar diagrams. We extendKhovanov’s graphical construction to derived categories of smooth andprojective varieties or, more generally, to categories having a Serrefunctor. In our case, the underlying lattice will be the (numerical)Grothendieck group of the category. We also obtain a 2-representationof our Heisenberg category on a categorical analogue of the Fockspace. Joint work with Clemens Koppensteiner and Timothy Logvinenko.

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