C*-simplicity and the Poisson boundary

Abstract: A connection between the Furstenberg boundary and $C^*$-simplicity of groups was a major breakthrough of the previous decade by Kalantar and Kennedy. The furstenberg boundary is a topological object associated with a group. The Poisson boundary is a measurable object, associated with a pair of a group and a probability measure on the group, that describes the asymptotic behaviour of the random walk on the group. I will talk about a connection between $C^*$-simplicity and the Poisson boundary, namely, that a countable group is $C^*$-simple iff its natural action on the Poisson boundary is essentially free for a generic measure on the group.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper )

---

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.

***** We're transitioning to a new platform google meet. Please bear with us and we apologize for the inconvenience! ****

---