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SUMMARY:Homological stability of moduli spaces via E_k-algebras - Ismael S
 ierra (University of Cambridge)
DTSTART:20230616T104500Z
DTEND:20230616T114500Z
UID:TALK199927@talks.cam.ac.uk
DESCRIPTION:\n\n\nI will present some homological stability results for di
 ffeomorphism groups of the manifolds $W_{g\,1}:=D^{2n} \\# (S^n \\times S^
 n)^{\\#g}$ and spin mapping class groups of surfaces.&nbsp\;\nThe proof of
  these results is based on the cellular E_k algebra method introduced by G
 alatius--Kupers--Randal-Williams\, which enables the use of various homoto
 py theoretic tools to study homological stability.&nbsp\;&nbsp\;\nI will e
 xplain the main steps of this method and how it applies to both diffeomorp
 hism groups and spin mapping class groups\, focusing on some underlying id
 eas and computations that can also be applied in more general contexts.&nb
 sp\;\n\n\n
LOCATION:Seminar Room 1\, Newton Institute
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