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SUMMARY:Minicourse: Classifiability of crossed products (2) - Gabor Szabo 
 (KU Leuven)
DTSTART:20250701T083000Z
DTEND:20250701T100000Z
UID:TALK233158@talks.cam.ac.uk
DESCRIPTION:In this mini course we will survey the existing approaches and
  theorems to answer the fundamentalquestion whether a simple nuclear C*-al
 gebra arising as the crossed product of a topological dynamicalsystems fal
 ls within the scope of classification theory. As a consequence of the gene
 ral structure theory fornuclear C*-algebras\, we now know that the key iss
 ue lies in whether such a crossed product satisfies oneof the regularity p
 roperties appearing in the Toms-Winter conjecture. Starting from a basic i
 ntroductionto crossed product C*-algebras\, we will first set up this gene
 ral question in more rigorous terms\, andconsider at least two perspective
 s from which it can be studied. The first perspective is given by theroute
  of verifying that the crossed product has finite nuclear dimension\, whic
 h leads us to concepts suchas Hirshberg-Winter-Zacharias&rsquo\; Rokhlin d
 imension for group actions or Guentner-Willet-Yu&rsquo\;s dynamicasymptoti
 c dimension for etale groupoids. The second perspective is given by the ro
 ute of verifying that &acute\;the crossed product is Jiang-Su stable\, whi
 ch leads us to concepts like Matui-Kerr&rsquo\;s almost finiteness forgrou
 p actions. We shall discuss these concepts\, go through a selection of the
  state of the art theorems\,and (time permitting) take a closer look at sp
 ecial cases to illustrate these theorems.Recommended further reading (this
  will not be assumed)&bull\; For classification theory and the Toms-Winter
  conjecture\, it can be instructive to read parts ofStrung&rsquo\;s book t
 itled &rdquo\;An introduction to C*-algebras and the classification progra
 m&rdquo\; (in particular the last chapter) or the introduction of the pre
 print by Carrion et al titled &rdquo\;Classifying *-homomorphisms I: Unita
 l simple nuclear C*-algebras&rdquo\; (arXiv:2307.06480).&bull\; For an int
 roduction to crossed products\, groupoid C*-algebras and Rokhlin dimension
 \, the readercan consult the book by Sims-Szabo-Williams titled &rdquo\;Op
 erator Algebras and Dynamics: Groupoids\, &acute\;Crossed products\, and R
 okhlin dimension&rdquo\;.&nbsp\;
LOCATION:External
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