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SUMMARY:Bivariant and Dynamical Versions of the Cuntz Semigroup - Joachim 
 Zacharias (University of Glasgow)
DTSTART:20170606T114500Z
DTEND:20170606T124500Z
UID:TALK72933@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:&nbsp\;The Cuntz Semigroup is an invariant for C*-algebras com
 bining K-theoretical and tracial information. It can be regarded as a C*-a
 nalogue of the Murray-von-Neumann semigroup of projections of a von Neuman
 n algebra. The Cuntz semigroup plays an increasingly important role in the
  classification of simple C*-algebras. We propose a bivariant version of t
 he Cuntz Semigroup based on equivalence classes of order zero maps between
  a given pair of C*-algebras. The&nbsp\;resulting bivariant theory behaves
  similarly to Kasparov&#39\;s KK-theory: it contains the ordinary Cuntz Se
 migroup as a special case just as KK-theory contains K-theory and&nbsp\;ad
 mits a composition product. It can be described in different pictures simi
 larly to the classical Cuntz Semigroup and behaves well with respect to va
 rious stabilisations. Many properties of the ordinary Cuntz Semigroup have
  bivariant counterparts. Whilst in general hard to determine\, the bivaria
 nt Cuntz Semigroup can be computed in some special cases. Moreover\, it ca
 n be used to classify stably finite algebras in analogy to the Kirchberg-P
 hillips classification of simple purely infinite algebras via KK-theory. W
 e also indicate how an equivariant version of the bivariant Cuntz Semigrou
 p can be defined\,&nbsp\;at least for compact groups. If time permits\, we
  discuss recent work in progress on a version of the Cuntz Semigroup for d
 ynamical systems\, more precisely\, groups&nbsp\;acting on compact spaces\
 , with potential applications to classifiability of crossed products. (Joi
 nt work with Joan Bosa\, Gabriele Tornetta.)<br><br><br><br>
LOCATION:Seminar Room 2\, Newton Institute
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