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X-WR-CALNAME:QM Research Seminar: The Heisenberg category of a category
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DTSTAMP:20260602T163052Z
DTSTART:20261028T030000
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DESCRIPTION:[b]Speaker: Timothy Logvinenko[/b] (Cardiff University) [nl][n
 l]\n[b]Abstract:[/b][nl]\nIn 90s Nakajima and Grojnowski identified the t
 otal cohomology of the Hilbert schemes of points on a smooth projective s
 urface with the Fock space representation of the Heisenberg algebra assoc
 iated to its cohomology lattice. Later\, Krug lifted this to derived cate
 gories and generalised it to the symmetric quotient stacks of any smooth 
 projective variety.\n\nOn the other hand\, Khovanov introduced a categori
 fication of the free boson Heisenberg algebra\, i.e. the one associated t
 o the rank 1 lattice. It is a monoidal category whose morphisms are descr
 ibed by a certain planar diagram calculus which categorifies the Heisenbe
 rg relations. A similar categorification was constructed by Cautis and Li
 cata for the Heisenberg algebras of ADE type root lattices.\n\nWe show ho
 w to associate the Heisenberg 2-category to any smoooth and proper DG cat
 egory and then define its Fock space 2-representation. This construction 
 unifies all the results above and extends them to what can be viewed as t
 he generality of arbitrary noncommutative smooth and proper schemes.\n[nl
 ]\n[nl]
DTEND:20240325T150000Z
DTSTAMP:20260602T163052Z
DTSTART:20240325T140000Z
LOCATION:Syddansk Universitet\, Campusvej 55\, 5230\, Odense M
SEQUENCE:0
SUMMARY:QM Research Seminar: The Heisenberg category of a category
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