In 2003, a big bang occurred when the famous manuscript by Kechris, Pestov, and Todorcevic was uploaded to Arxiv, in which occurred a collusion between topological dynamics, Ramsey theory, and model theory, that left these fields not as they were before - the paper creates a strong link between properties of the automorphism group of a structure (as a topological group) and combinatorial properties of colourings of the same structure.
In this talk, I will survey the history leading to that bang, from Ramsey himself, through Ehrenfeucht and Mostowsky (and from the other side from Mitchell, through Herer, Christensen, Gromov, Milman, Frustenberg, Weiss, Glasner, up to Pestov) and finally Kechris, Pestov, and Todorcevic.
I will also survey applications in modern model theory, and, as time allows, a non-empty set of recent contributions to which I’m proud to be part of.