Stability and Testability

I will describe how basic ergodic theory can be used to prove that certain amenable groups are stable. I will demonstrate our method by showing that lamplighter groups are stable. Another uncountably infinite family to which our method applies are...

Determining whether or not a given finitely generated group is permutation stable is in general a difficult problem. In this talk we discuss work of Becker, Lubotzky and Thom which gives, in the case of amenable groups, a necessary and sufficient...

In this lecture I will describe the three concepts appearing in the title and how they connect with each other.

The aim of this talk is to show that C*-algebras are useful for studying stability of groups. In particular we will discuss some obstructions for Hilbert-Schmidt stability of groups, obtain a complete characterization of Hilbert-Schmidt stability...

In his seminal paper from 1973, Garland introduced a machinery for proving vanishing of group cohomology for groups acting on Bruhat-Tits buildings. This machinery, known today as “Garland’s method”, had several applications as a tool for proving...

Several well-known open questions (such as: are all groups sofic/hyperlinear?) have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n)Sym(n) (in the sofic case) or the finite dimensional...

Let C be a class of groups. (For example, C is a class of all finite groups, or C is a class of all finite symmetric groups.) I give a definition of approximations of a group G by groups from C. For example, the groups approximable by symmetric...

In this talk I will present a joint work with Arie Levit and Yair Minsky on flexible stability of surface groups. The proof will be geometric in nature and will rely on an analysis of branched covers of hyperbolic surfaces. Along the way we will see...