Apparaît dans la collection : 2018 - T1 - WS1 - Model theory and combinatorics

The connection between Ramsey theory and topological dynamics goes back at least to Furstenberg who used dynamical systems of the group of integers to derive a new proof of Van Der Waerden’s theorem. More recently, Kechris, Pestov, and Todorcevic developed a new correspondence between structural Ramsey theory and certain universal dynamical systems of the corresponding automorphism groups. I will survey what is known in the area as well as the most important open questions. I will also discuss some recent generalizations of the framework to the continuous setting.