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SUMMARY:Aidan Sims (University of Wollongong)
DTSTART:20230217T040000Z
DTEND:20230217T050000Z
DTSTAMP:20260423T021445Z
UID:SiN/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SiN/53/">K-t
 heoretic duality for self-similar groupoids</a>\nby Aidan Sims (University
  of Wollongong) as part of Symmetry in Newcastle\n\n\nAbstract\nA K-theore
 tic duality for C*-algebras is\, roughly speaking\, a particularly nice is
 omorphism of the K-theory groups of each with the K-homology groups of the
  other. They are generalisations of Poincare duality for manifolds\, and i
 n that vein\, they often help to compute algebraic or analytic K-theory in
 variants in terms of more-tractable topological information. Under some te
 chnical hypotheses\, Nekrashevych established a K-theoretic duality betwee
 n the C*-algebra of a self-similar group and a related C*-algebra associat
 ed to a limit space that resembles the way that real numbers are represent
 ed by decimal expansions. I will discuss how Nekrashevych’s limit space 
 is constructed\, focussing on elementary but instructive examples to keep 
 things concrete\, and sketch out how to use it to describe a K-theoretic d
 uality that helps in computing K-theory for self-similar groupoid C*-algeb
 ras. I won’t assume any background in any of this stuff. This is joint w
 ork with Brownlowe\, Buss\, Goncalves\, Hume and Whittaker.\n
LOCATION:https://researchseminars.org/talk/SiN/53/
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