Stability and Testability

Approximations of infinite groups

Goulnara Arzhantseva

We discuss various (still open) questions on approximations of finitely generated groups, focusing on finite-dimensional approximations such as residual finiteness and soficity. We survey our results on the existence, stability and quantification of...

Ultrametric stability problems

Francesco Fournier Facio

We study stability problems with respect to families of groups equipped with bi-invariant ultrametrics, that is, metrics satisfying the strong triangle inequality. This property has very strong consequences, and this form of stability behaves very...

Some years ago, I proved with Shulman and Sørensen that precisely 12 of the 17 wallpaper groups are matricially stable in the operator norm. We did so as part of a general investigation of when group C?C?-algebras have the semiprojectivity and weak...

A recent result of Becker, Lubotzky and Thom characterizes, for amenable groups, permutation stability in terms of co-soficity of invariant random subgroups (IRS). We will explain that for a class of amenable groups acting on rooted trees, including...