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SUMMARY:Itamar Vigdorovich (University of California\, San Diego)
DTSTART:20250409T190000Z
DTEND:20250409T200000Z
DTSTAMP:20260420T053057Z
UID:NYC-NCG/192
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/192/
 ">Structural properties of reduced $C^∗$-algebras associated with higher
 -rank lattices</a>\nby Itamar Vigdorovich (University of California\, San 
 Diego) as part of Noncommutative geometry in NYC\n\n\nAbstract\nWe present
  the first examples of higher-rank lattices whose reduced $C^*$-algebras s
 atisfy strict comparison\, stable rank one\, selflessness\, uniqueness of 
 embeddings of the Jiang--Su algebra\, and allow explicit computations of t
 he Cuntz semigroup. This resolves a question raised in recent groundbreaki
 ng work of Amrutam\, Gao\, Kunnawalkam Elayavalli\, and Patchell\, in whic
 h they exhibited a large class of finitely generated non-amenable groups s
 atisfying these properties. Our proof relies on quantitative estimates in 
 projective dynamics\, crucially using the exponential mixing for diagonali
 zable flows. As a result\, we obtain an effective mixed-identity-freeness 
 property\, which\, combined with V. Lafforgue's rapid decay theorem\, yiel
 ds the desired conclusions.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/192/
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