On subsets with no arithmetic progressions

ABSTRACT

For $N\in \mathbb{N}$, let $\nu(N)$ be the maximal cardinality of a subset of \{1,\ldots,N\} that contains no
arithmetic progression of length 3. Finding upper and lower bounds for $\nu(N)$ has been a challenging problem for decades.

In this talk I will survey this problem and present a proof of a theorem by Behrend in the 40’s, that gave a surprising lower bound to $\nu(N)$.

Posted on Mar 28, 2019 in Dynamical Systems, Seminars