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SUMMARY:Clément Dell'Aiera (ENS Lyon)
DTSTART:20210217T200000Z
DTEND:20210217T210000Z
DTSTAMP:20260420T052929Z
UID:NYC-NCG/40
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/40/"
 >Dynamic asymptotic dimension and homology</a>\nby Clément Dell'Aiera (EN
 S Lyon) as part of Noncommutative geometry in NYC\n\n\nAbstract\nGroupoid 
 homology has attracted increasing attention from from the topological dyna
 mics and operator algebras communities following the work of Matui. Matui'
 s HK conjecture predicts that the K-theory groups of the reduced C*-algebr
 a of a minimal essentially principal ample groupoid coincides with its hom
 ology groups. We prove that homology of principal ample groupoids vanish i
 n degree above its dynamical asymptotic dimension\, a notion of dimension 
 from topological dynamics. We deduce several consequences: Matui's HK conj
 ecture holds for low dimensional principal ample groupoids\, and classific
 ation of their reduced C*-algebra. (Joint work with Christian Bonicke\, Ja
 mie Gabe and Rufus Willett)\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/40/
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