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SUMMARY:Fusion system\, p-completed classifying spaces\, loops\, (co)singu
 larity categories - David Benson  (University of Aberdeen)
DTSTART:20220623T150000Z
DTEND:20220623T160000Z
UID:TALK175628@talks.cam.ac.uk
DESCRIPTION:Cochains on the $p$-completed classifying space of a finite gr
 oup (or more generally\, a fusion system)\, and chains on its loop space\,
  are Koszul dual objects with interesting representation theory. My intent
 ion is to talk about the singularity and cosingularity categories of these
  objects.\nI shall discuss fusion systems\, linking systems\, Chermak's th
 eorem\, classifying spaces\, Bousfield--Kan $p$-completion\, the loop spac
 e\, $A_\\infty$ structures\, Koszul duality\, the derived category\, the s
 ingularity category\, the cosingularity category\, the role of the nucleus
 \, and some conjectures. I shall concentrate on some examples\, coming fro
 m finite groups with cyclic Sylow $p$-subgroups\, and the tame representat
 ion type cases in characteristic two.
LOCATION:Seminar Room 2\, Newton Institute
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