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SUMMARY:On Sharpness for Fusion Systems - Valentina Grazian (Università d
 egli Studi di Milano - Bicocca)
DTSTART:20220610T120000Z
DTEND:20220610T130000Z
UID:TALK175391@talks.cam.ac.uk
DESCRIPTION:&nbsp\;\nFusion systems are structures that encode the propert
 ies of conjugation between p-subgroups of a group\, for p any prime number
 \, and represent the modern approach to the study of the p-local structure
  of finite groups. To every saturated fusion system F defined on the p-gro
 up S\, one can associate a topological space BF that plays the role that c
 lassifying spaces play for finite groups. In analogy with finite groups\, 
 it is possible to reconstruct such a classifying space BF by gluing togeth
 er classifying spaces BP\, where P runs over a suitably chosen collection 
 of subgroups of S. In 1998\, Dwyer showed that if G is a finite group and 
 the collection considered is the one of p-centric subgroups of G\, then th
 e corresponding homology decomposition is sharp\, making it easier to desc
 ribe the classifying space BG. In 2015 Diaz and Park established a conject
 ure that extends Dwyer&rsquo\;s sharpness result in two ways: they conside
 r fusion systems instead of groups and Mackey functors in place of cohomol
 ogy functors.
LOCATION:Seminar Room 2\, Newton Institute
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