A Survey on Structural Ramsey Theory and Topological Dynamics with the Kechris-Pestov-Todorcevic Correspondence in Mind

Lionel Nguyen Van Thé

The article [27], published in 2005 by Kechris, Pestov and Todorcevic, established a surprising correspondence between structural Ramsey theory and topological dynamics. As an immediate consequence, it triggered a new interest for structural Ramsey theory. The purpose of the present paper is to present a self-contained survey of the corresponding developments.