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SUMMARY:Counting conjectures for fusion systems - Jason Semeraro (Universi
 ty of Leicester\, Heilbronn Institute\, University of Bristol)
DTSTART:20220511T102000Z
DTEND:20220511T105000Z
UID:TALK172802@talks.cam.ac.uk
DESCRIPTION:An ℓ-compact group is a homotopical analogue of a compact Li
 e group whose homotopy fixed point spaces are classifying spaces of fusion
  systems of finite groups of Lie type. After motivating the study of weigh
 ts for fusion systems\, I will report on the first part of ongoing joint w
 ork with Gunter Malle and Radha Kessar investigating weights associated to
  homotopy fixed point spaces of ℓ-compact groups. We showed that certain
  equations predicted by local-global conjectures in the modular representa
 tion theory of finite groups of Lie type continue to hold in the ℓ-compa
 ct setting. If time permits\, I will show these equations hold even more g
 enerally in the category of ℓ-local compact groups\, pointing towards so
 me yet unknown structural explanation for them purely in the framework of 
 fusion systems.
LOCATION:Seminar Room 1\, Newton Institute
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