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SUMMARY:Dimitrios Gerontogiannis
DTSTART:20210215T150000Z
DTEND:20210215T160000Z
DTSTAMP:20260423T021313Z
UID:GOBA/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GOBA/20/">Sm
 ooth algebras associated to Smale spaces and extensions by Schatten ideals
 </a>\nby Dimitrios Gerontogiannis as part of Groups\, Operators\, and Bana
 ch Algebras Webinar\n\n\nAbstract\nIn the 1980's\, Douglas initiated the s
 tudy of smooth extensions of C*-algebras\; C*-algebraic extensions by the 
 ideal of compact operators that on certain dense *-subalgebras (in cases B
 anach) reduce to algebraic extensions by Schatten ideals. Douglas studied 
 smooth extensions of C(X)\, for X being a finite complex. Shortly after\, 
 Douglas and Voiculescu studied the case of sphere extensions. In the nonco
 mmutative setting\, examples of C*-algebras with a pervading presence of s
 mooth extensions include the Cuntz-Krieger algebras (Goffeng-Mesland)\, an
 d crossed product C*-algebras formed by Gromov hyperbolic groups acting on
  their boundary (Emerson-Nica). In this talk I will present the notion of 
 smoothness in C*-algebras and that the smooth extensions of Ruelle algebra
 s (higher dimensional analogues of Cuntz-Krieger algebras) associated to S
 male spaces\, are generic in some sense. The smoothness of Ruelle algebras
  has interesting connections with the Hausdorff dimension of the underlyin
 g Smale space. This research is part of my PhD thesis.\n
LOCATION:https://researchseminars.org/talk/GOBA/20/
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