Banach representations of dynamical systems and model theory

It is well-known that the automorphism group of an omega-categorical structure encodes all model-theoretic information about the structure. Recently, an interesting correspondence has been discovered between properties of the theory (stability, omega-stability, NIP) and classes of Banach spaces on which certain dynamical systems (the automorphism group acting on type spaces over the model) can be represented. In the stable case, those dynamical systems also carry the structure of a semigroup that can be exploited. I will discuss what is known about this correspondence as well as some open questions. This is joint work with Itaï Ben Yaacov and Tomás Ibarlucía.Non UBCUnreviewedAuthor affiliation: Université Paris 7Facult