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SUMMARY:Makoto Yamashita (University of Oslo)
DTSTART:20220302T150000Z
DTEND:20220302T160000Z
DTSTAMP:20260420T053048Z
UID:NYC-NCG/88
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/88/"
 >Homology and K-theory of dynamical systems</a>\nby Makoto Yamashita (Univ
 ersity of Oslo) as part of Noncommutative geometry in NYC\n\n\nAbstract\nA
  theory of homology for étale groupoids was developed by Crainic and Moer
 dijk based on simplicial structure of nerves of groupoids\, as a companion
  to Haeflier's theory of cohomology for groupoids. We relate this to anoth
 er (co)homology of groupoids\, namely the operator K-groups of the associa
 ted convolution algebra\, when the base is totally disconnected. Such a co
 nnection was conjectured by Matui through his study of Cantor dynamical sy
 stems. Our proof is based on the triangulated categorical structure of gro
 upoid equivariant KK-theory\, following the categorical approach to the Ba
 um-Connes conjecture by Meyer and Nest. Along the way we uncover the close
  connection to Putnam's homology theory for hyperbolic dynamical systems (
 Smale spaces). Based on joint works with Valerio Proietti.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/88/
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