Sparse graphs, topological dynamics and structural Ramsey theory

David Evans, Imperial College London. Part of the logic seminar series.

I will consider automorphism groups of countable structures acting continuously on compact spaces: the viewpoint of topological dynamics. A beautiful paper of Kechris, Pestov and Todorcevic makes a connection between this and the 'structural Ramsey theory' of Nesetril, Rodl and others infinite combinatorics. I will describe some results and questions in the area and say how some 'sparse' graphs constructed by Hrushovski to answer a variety of questions in model theory provide answers to some of these questions (but then raise more questions).

This is joint work with Hubicka and Nesetril.

David Evans, Imperial College London