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SUMMARY:Nivedita (University of Oxford)
DTSTART:20250423T150000Z
DTEND:20250423T163000Z
DTSTAMP:20260422T174306Z
UID:tandg/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/tandg/31/">B
 icommutant categories from conformal nets</a>\nby Nivedita (University of 
 Oxford) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbs
 tract\nTwo-dimensional chiral conformal field theories (CFTs) admit three 
 distinct mathematical formulations: vertex operator algebras (VOAs)\, conf
 ormal nets\, and Segal (functorial) chiral CFTs. With the broader aim to b
 uild fully extended Segal chiral CFTs\, we start with the input of a confo
 rmal net.\n\nIn this talk\, we focus on presenting three equivalent constr
 uctions of the category of solitons\, i.e. the category of solitonic repre
 sentations of the net\, which we propose is what theory (chiral CFT) assig
 ns to a point. Solitonic representations of the net are one of the primary
  class of examples of bicommutant categories (a categorified analogue of a
  von Neumann algebras). The Drinfel’d centre of solitonic representation
 s is the representation category of the conformal net which has been studi
 ed before\, particularly in the context of rational CFTs (finite-index net
 s). If time permits\, we will briefly outline ongoing work on bicommutant 
 category modules (which are the structures assigned by the Segal Chiral CF
 T at the level of 1-manifolds)\, hinting towards a categorified analogue o
 f Connes fusion of von Neumann algebra modules.\n\n(Bicommutant categories
  act on W*-categories analogous to von Neumann algebras acting on Hilbert 
 spaces.)\n
LOCATION:https://researchseminars.org/talk/tandg/31/
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