Stability and Testability

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 differently from the other ones that we saw throughout the seminar. Many results can be established in full generality, but we will focus on a p-adic analogue of Ulam stability, where the family of approximating groups is $GL_n(Z_p)$.