Both talks will be given by Oren Becker.
9:00 - 10:50
Title: Proving stability via hyperfiniteness, graph limits and invariant random subgroups

Abstract: We will discuss stability in permutations, mostly in the context of amenable groups. We will characterize stable groups among amenable groups in terms of their invariant random subgroups. Then, we will introduce graph limits and hyperfinite graphings (and some theorems about them), and show how the aforementioned characterization of stability follows.

14:00 - 16:00
Title: Examples of (non-)stable groups, and more

Abstract: We will use the characterization proved in the morning talk to prove that various groups (hence equations) are stable or non-stable. According to the way things go, we may either explain the proofs of some of the tools used throughout the talks, or talk about stability of groups with Kazhdan's Property (T).