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SUMMARY:Minicourse: groupoid C*-algebras and Cartan subalgebras (1) - Anna
   Duwenig (University of New South Wales)
DTSTART:20250630T123000Z
DTEND:20250630T140000Z
UID:TALK233152@talks.cam.ac.uk
DESCRIPTION:The focus of this minicourse is the construction of C*-algebra
 s from groupoids on the one hand\, andthe reconstruction of groupoids from
  C*-algebras with Cartan subalgebras on the other hand. Guided bycommon ex
 amples\, we will start with a basic introduction to topological groupoids 
 and so-called twistsover them. In the special case of etale groupoids\, we
  will then see how to build the associated twisted &acute\;reduced C*-alge
 bra\, and how Kumjian&ndash\;Renault theory provides an inverse process: i
 f the groupoid hasno (open) abelian subgroupoids (ie\, the groupoid is &ld
 quo\;effective&rdquo\;)\, then one can reconstruct it from itsC*-algebra t
 ogether with a &ldquo\;canonical&rdquo\; abelian subalgebra. If time permi
 ts\, we will have a look at thenon-effective situation.Futher prepartory r
 eading (this will not be assumed) In much of the first half of this minico
 urse\, I willbe following Part II of the book &ldquo\;Operator Algebras an
 d Dynamics: Groupoids\, Crossed products\, andRokhlin dimension&rdquo\; by
  Sims&ndash\;Szabo&ndash\;Williams. The interested participant can find fu
 rther information &acute\;on groupoid C*-algebras in Williams&rsquo\; book
  &ldquo\;A Tool Kit for Groupoid C*-Algebras.&rdquo\;&nbsp\;
LOCATION:External
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