Strong ergodicity, projections and Markov operators

Abstract: The aim of this talk is to illustrate how some insights from the theory of Markov processes can be adapted to prove that certain projections belong to "Roe-like" C*-algebras of dynamical origin. Given an action of a countable discrete group on a measure space, one may define a C*-algebra by taking the closure of an algebra of operators with finite propagation. I will explain that this C*-algebra contains a certain natural family of rank-one projections if and only if the action is strongly ergodic. This result can be used to construct more counterexamples to the coarse Baum-Connes conjecture.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | video )

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Noncommutative geometry in NYC

Series comments: Noncommutative Geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. Our seminar welcomes talks in Number Theory, Geometric Topology and Representation Theory linked to the context of Operator Algebras. All talks are kept at the entry-level accessible to the graduate students and non-experts in the field. To join us click meet.google.com/zjd-ehrs-wtx (5 min in advance) and igor DOT v DOT nikolaev AT gmail DOT com to subscribe/unsubscribe for the mailing list, to propose a talk or to suggest a speaker. Pending speaker's consent, we record and publish all talks at the hyperlink "video" on speaker's profile at the "Past talks" section. The slides can be posted by providing the organizers with a link in the format "myschool.edu/~myfolder/myslides.pdf". The duration of talks is 1 hour plus or minus 10 minutes.

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