Aris Papadopoulos (Leeds)

Model Theory and Combinatorics or (The Unexpected Virtue of Tameness)

Hrushovski once called model theory the "geography of tame mathematics"; a quote which may make no sense if you're not a model theorist (or if you are, in fact, a geographer). I will try to explain this point of view, by discussing how model theorists draw "dividing lines" separating the tame theories from the wild ones and illustrating this through examples from combinatorics.

The aim of this talk is to provide a gentle introduction to some recent developments in the area. Perhaps ambitiously, I will try to (briefly and informally) discuss three very different topics: (i) Szemerédi Regularity in stable (due to Malliaris-Shelah), NIP (due to Fox, Pach and Suk), and distal structures (due to Chernikov and Starchenko); (ii) Algorithmic tameness in hereditary classes of relational structures (joint work with S. Braunfeld, A. Dawar and I. Eleftheriadis); and (iii) Zarankiewicz's problem in semilinear (due to Basit, Chernikov, Starchenko, Tao and Tran) and semibounded (joint work with P. Eleftheriou) o-minimal structures.