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SUMMARY:Hopf algebras\, quantum groups and monoidal categories (UCL-ULB-VU
 B seminar)
DTSTART:20260908T120000Z
DTEND:20260908T141500Z
DTSTAMP:20260917T142300Z
UID:indico-event-5892@agenda.irmp.ucl.ac.be
DESCRIPTION:Speakers: Daniel Bermudez (Universität Bonn)\, Victor Zhang (
 University of New South Wales)\n\n14:00 - 14:50: Victor Zhang (University 
 of New South Wales):  Diagrammatic Lusztig--Vogan Categories\n \n\nAbstr
 act:  The Kazhdan--Lusztig conjecture (1979) relates the decomposition nu
 mbers of complex semisimple Lie algebra representations in terms of a spec
 ial change of basis in the Hecke algebra. In a subsequent proof of the con
 jecture\, a complete diagrammatic language was developed for the categorif
 ication of the Hecke algebra\, the category of Soergel bimodules\, followi
 ng the effort of various people throughout the 2000s and 2010s. The theory
  of real reductive Lie groups carries a result analogous to the KL-conject
 ure by Lusztig and Vogan (1983)\, that the Lusztig--Vogan modules over the
  Hecke algebra capture composition multiplicities of $(\\mathfrak{g}\,K)$-
 modules. We will motivate diagrammatic tools in mathematics and present th
 e beginnings of a diagrammatic theory for a categorification of these Lusz
 tig--Vogan modules.\n\n \n15:10 - 16:00: Daniel Bermudez (Universität Bo
 nn):  The A_infty Drinfeld centralizer as a homotopy limit\n \n\nAbstrac
 t: By a theorem by Street\, the Drinfeld center can be described as a bili
 mit of a (truncated) cosimplicial diagram. I will explain how to generaliz
 e this picture to dg-categories. Elias and Hogancamp recently introduced a
 n A_infty centralizer of a monoidal dg-category\, defined through explicit
  data. I will show that this centralizer arises as a homotopy limit of a c
 osimplicial diagram built from A_infinity functor categories.  As a conse
 quence\, we conclude that the A_infty centralizer is a concrete dg-model f
 or Lurie's infty-categorical centralizer on the infty-category of dg-categ
 ories\, and thus can be inherited with an E2-algebra structure\, i.e. a br
 aiding. \n\n\nhttps://agenda.irmp.ucl.ac.be/event/5892/
LOCATION:B/2nd floor-B.203 - Seminar room (Marc de Hemptinne (chemin du Cy
 clotron\, 2\, Louvain-la-Neuve))
URL:https://agenda.irmp.ucl.ac.be/event/5892/
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