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SUMMARY:Timothy Logvinenko (Cardiff University)
DTSTART:20211026T180000Z
DTEND:20211026T190000Z
DTSTAMP:20260423T024613Z
UID:AG-Davis/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AG-Davis/37/
 ">The Heisenberg category of a category</a>\nby Timothy Logvinenko (Cardif
 f University) as part of UC Davis algebraic geometry seminar\n\n\nAbstract
 \nIn 90s Nakajima and Grojnowski identified the total cohomology of the Hi
 lbert schemes of points on a smooth projective surface with the Fock space
  representation of the Heisenberg algebra associated to its cohomology lat
 tice. Later\, Krug lifted this to derived categories and generalized it to
  the symmetric quotient stacks of any smooth projective variety.\n\nOn the
  other hand\, Khovanov introduced a categorification of the free boson Hei
 senberg algebra\, i.e. the one associated to the rank 1 lattice. It is a m
 onoidal category whose morphisms are described by a certain planar diagram
  calculus which categorifies the Heisenberg relations. A similar categorif
 ication was constructed by Cautis and Licata for the Heisenberg algebras o
 f ADE type root lattices.\n\nWe show how to associate the Heisenberg 2-cat
 egory to any smoooth and proper DG category and then define its Fock space
  2-representation. This construction unifies all the results above and ext
 ends them to what can be viewed as the generality of arbitrary noncommutat
 ive smooth and proper schemes.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/37/
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