Representation theory of non-Archimedean Polish groups and dissociation

For a countable homogeneous structure M, a natural question in representation theory is the classification of unitary representations of the Polish, non-archimedean group Aut(M). This question was completely answered by Tsankov for ω-categorical structures. In joint work with R. Barritault and C. Jahel, we generalize this result and go beyond ω-categoricity by addressing structures such as the integral/rational Urysohn space and the integral/rational universal diversity. We will explain how the notion of dissociation, a structural property of unitary representation for Polish non-archimedean groups, is used in our work. No background knowledge of representation theory will be assumed for this talk.