seminar Topological Dynamics and Model Theory

Topological dynamics studies continuous actions of topological groups. Key concepts include (extreme) amenability, universal minimal flows, and the Ellis semigroup. The relevance of topological dynamics to model theory has become increasingly clear over the last two decades. The connection arises both via the automorphism group of a structure and via groups definable in a structure. There is now a substantial literature on the fruitful interactions between the two subjects, with highlights including reinterpretations of the Kechris-Pestov-Todorcevic correspondence, which connects universal minimal flows and Ramsey theory, and the correspondences between model-theoretic stability and weakly almost periodic functions, and between NIP and tameness of a dynamical system. Moreover, there are applications to model-theoretic connected components of definable groups and Lascar's Galois group of a theory, which itself has applications in the study of approximate subgroups. This seminar will explore these connections.

Kurs im HIS-LSF