Franceso Fournier-Facio - Ulam stability of Thompson groups

This talk was part of the Workshop on "Geometric and Asymptotic Group Theory with Applications 2023 - Groups and Dynamics" held at the ESI July 17 — 21, 2023.

Ulam stability is a rigidity property for discrete groups that can be informally stated as: all approximate (finite-dimensional unitary) representations are just small perturbations of true representations. Glebsky-Lubotzky-Monod-Rangarajan recently proved Ulam stability of (almost) all lattices in higher rank Lie groups. Their proof introduces a new cohomology theory, called asymptotic cohomology, which can be seen as a nonstandard-analytic version of bounded cohomology. I will give a brief informal introduction to asymptotic cohomology, and explain how it can also be used to prove Ulam stability of Thompson's groups F, T and V. This is joint work with Bharatram Rangarajan.