### Seminar talk by Salomon: Combinatorial and operator algebraic aspects of proximal actions

#### by Orr Shalit

The Operator Algebras and Operator Theory Seminar is back (sort of). This semester we will have the seminar on Thursdays 15:30 (Israel time) about once in a while. Please send me an email if you want to join the mailing list and get the link for the zoom meetings. Here are the details for our first talk :

**Title: Combinatorial and operator algebraic aspects of proximal actions**

**Speaker: Guy Salomon** (Weizmann Institute)

**Time: **15:30-16:30,Thursday Nov. 12, 2020

(Zoom room will open about ten minutes earlier, and the talk will begin at 15:30)

**Zoom link:** email me.

**Abstract:**

An action of a discrete group on a compact Hausdorff space is called * proximal* if for every two points and of there is a net such that , and

*if the natural action of on the space of probability measures on is proximal. The group is called*

**strongly proximal**

*strongly***if all of its proximal actions have a fixed point and**

*amenable***if all of its strongly proximal actions have a fixed point.**

*amenable*In this talk I will present relations between some fundamental operator theoretic concepts to proximal and strongly proximal actions, and hence to amenable and strongly amenable groups. In particular, I will focus on the C*-algebra of continuous functions over the universal minimal proximal -flow and characterize it in the category of -operator-systems.

I will then show that nontrivial proximal actions of can arise from partitions of into a certain kind of “large” subsets. If time allows, I will also present some relations to the Poisson boundaries of . The talk is based on a joint work with Matthew Kennedy and Sven Raum.