I will present a combinatorial property---finite VC-dimension---which appeared independently in various parts of mathematics.

In model theory it is called "NIP" and is used notably in the study of ordered and valued fields. In probability theory, it is related to "learnable classes". In combinatorics, classes of finite VC-dimension behave a lot like families of convex subsets of euclidean space. I will also talk about Banach spaces and topological dynamics.

The talk will be accessible to postdocs of both programs.