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.
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 strongly proximal if the natural action of on the space of probability measures on is proximal. The group is called strongly amenable if all of its proximal actions have a fixed point and amenable if all of its strongly proximal actions have a fixed point.
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.