Submission date: 15 June 2021

Abstract:

We present a recent result of Ibarlucía stating that every Roelcke precompact Polish group has Kazdhan's property (T). This striking theorem builds on the characterization of Roelcke precompact Polish groups as automorphism groups of ℵ_0-categorical metric structures due to Ben Yaacov and Tsankov. We introduce the underlying concepts coming from model theory, and we outline Ibarlucía's proof in the (already new!) particular case of the group of measure-preserving transformations of a standard probability space.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 2106.08244: pdf, ps.