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SUMMARY:The Heisenberg category of a category [MPIM]
DTSTART:20260414T090000Z
DTEND:20260414T103000Z
DTSTAMP:20260418T103500Z
UID:indico-event-1208@math-events.uni-bonn.de
DESCRIPTION:Speakers: Timothy Logvinenko (Cardiff University)\n\nAbstract 
 Homotopy Theory Seminar\nIn 90s Nakajima and Grojnowski identified the tot
 al cohomology of the Hilbert schemes of points on a smooth projective surf
 ace with the Fock space representation of the Heisenberg algebra associate
 d to its cohomology lattice. Following a conjecture by Grojnowski\, Segal 
 and Wang extended this to any smooth projective variety by replacing Hilbe
 rt schemes with symmetric powers and cohomology with equivariant K-theory.
  Later\, Krug lifted this to the level of derived categories.\nOn the othe
 r hand\, Khovanov introduced a categorification of the free boson Heisenbe
 rg algebra\, i.e. the one associated a single point. It is a monoidal cate
 gory whose morphisms are described by a certain planar diagram calculus wh
 ich categorifies the Heisenberg relations. A similar categorification was 
 constructed by Cautis and Licata for the Heisenberg algebras of ADE type r
 oot lattices.\nWe show how to associate the Heisenberg 2-category to any s
 moooth and proper DG category and then define its Fock space 2-representat
 ion. This construction can be decategorified via K-theory or via Hochschil
 d homology. It unifies all the results above and extends them to what can 
 be viewed as the generality of arbitrary noncommutative smooth and proper 
 schemes.\n \n \n\nhttps://math-events.uni-bonn.de/event/1208/
LOCATION:MPIM\, Vivatsgasse\,  7 - Seminar Room (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1208/
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