The Heisenberg algebra of a vector space and Hochschild homology

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• Timothy Logvinenko, University of Cardiff
• Wednesday 30 April 2025, 14:15-15:15
• CMS MR13.

If you have a question about this talk, please contact Mark Gross.

In arXiv:2105.13334, Gyenge, Koppensteiner and Logvinenko constructed a 2-categorification of the Heisenberg algebra of any (possibly noncommutative) smooth projective variety, and decategorified it via Grothendieck group. In this talk, I will first give an overview of our 2-categorification and then explain how to decategorify it via the Hochschild homology HH_*, instead. Effectively, this means extending the decategorification map from a lattice in HH_0 to the whole Hochschild homology. The payoff is a direct generalisation to any smooth projective variety of Grojnowski and Nakajima’s original Heisenberg algebra action on the cohomology of Hilbert schemes of points on a surface.

This talk is part of the Algebraic Geometry Seminar series.

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