The Kővári-Sós-Turán theorem for stable hypergraphs

If you are even remotely combinatorially inclined, you will probably have heard of (and care about) the following question: "Given a graph G on n vertices which does not contain K_{2,2} as a subgraph, what is the maximum number of edges (as a function of n) G can have?” The first (and still relevant) answer to this question is “O(n^{3/2})” and was given by the Kővári-Sós-Turán theorem. In my talk, I will present a proof of a stronger version of the classical Kővári-Sós-Turán theorem for (model-theoretically) stable hypergraphs, but you probably already guessed that from the title. The proof will not go via the regularity lemma, but will instead be based on a coarse pseudofinite dimension argument, possibly of independent interest.