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We present a recent result of Ibarluc\'ia stating that every Roelckeprecompact Polish group has Kazhdan's property (T). This striking theorembuilds on the characterization of Roelcke precompact Polish groups asautomorphism groups of $\aleph_0$-categorical metric structures due to BenYaacov and Tsankov. We introduce the underlying concepts coming from modeltheory, and we outline Ibarluc\'ia's proof in the (already new!) particularcase of the group of measure-preserving transformations of a standardprobability space.

Property (T) for Roelcke precompact Polish groups (after Ibarluc\'ia, building on work of Ben Yaacov and Tsankov)