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SUMMARY:Computing high-dimensional group cohomology via duality - Benjamin
  Brueck (ETH Zurich)
DTSTART:20230120T134500Z
DTEND:20230120T144500Z
UID:TALK194413@talks.cam.ac.uk
CONTACT:76015
DESCRIPTION:In recent years\, duality approaches have yielded new results 
 about the high-dimensional cohomology of several groups and moduli spaces\
 , such as SL_n(Z) and $M_g$. I will explain the general strategy of these 
 approaches and survey results that have been obtained so far.\n\nTo give a
 n example\, I will first explain how Borel-Serre duality can be used to sh
 ow that the rational cohomology of SL_n(Z) vanishes near its virtual cohom
 ological dimension. This is based on joint work with Miller-Patzt-Sroka-Wi
 lson and builds on results by Church-Farb-Putman.\nI will then put this in
 to a more general context by giving an overview of analogous results for m
 apping class groups of surfaces\, automorphism groups of free groups and f
 urther arithmetic groups such as SL_n(O_k) and SP_2n(Z).
LOCATION:MR13
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