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Title: Polynomials, rank and cap sets

Péter Pál Pach

Budapest University of Technology

Abstract:

In this talk we will look at a variant of the polynomial method which was first used to prove that sets avoiding 3-term arithmetic progressions in groups like Z_4^n and F_q^n are exponentially small (compared to the size of the group). We will discuss lower and upper bounds for the size of the extremal subsets.  We will also mention some further applications of the method, for instance, the solution of the Erdős–Szemerédi theorem sunflower conjecture.