Thursday, October 11, 2018 - 4:15pm
Hebrew university of Jerusalem
Given two permutations A and B which “almost” commute, are they “close” to permutations A’ and B’ which really commute? Arzhantseva and Paunescu (2015) formalized this question and answered affirmatively. This can be viewed as a property of the equation XY=YX, and turns out to be equivalent to the following property of the group Z^2 = < X,Y | XY=YX >: Every “almost action” of Z^2 on a finite set is close to a genuine action of Z^2. This leads to the notion of stable groups.
We will describe a relationship between stability, invariant random subgroups and sofic groups, giving, in particular, a characterization of stability among amenable groups. We will then show how to apply the above in concrete cases to prove and refute stability of some classes of groups. Finally, we will discuss stability of groups with Kazhdan’s property (T), and some results on the quantitative aspect of stability.
Based on joint works with Alex Lubotzky, Andreas Thom and Jonathan Mosheiff.
Note the unsual day of the week (Thursday rather than Modnay)