Applications of model theory to the study of Roelcke precompact groups and their actions

Roelcke precompact groups are exactly the topological groups that can
be realized as automorphism groups of omega-categorical structures (in
continuous logic). In this talk, I will discuss a model-theoretic
framework for the study of those groups and their dynamical systems as
well as two concrete applications. The talk is based on joint work
with Itaï Ben Yaacov and Tomás Ibarlucía.