# Olof Sisask: Breaking the logarithmic barrier in Roth's theorem

**Time: **
Wed 2020-10-21 13.15 - 15.00

**Location: **
Zoom meeting ID: 657 9019 8929

**Participating: **
Olof Sisask, Stockholms universitet

### Abstract

We present an improvement to Roth's theorem on arithmetic progressions, showing that if A is a subset of \(\{1,2,...,N\}\) with no non-trivial three-term arithmetic progressions, then A has size at most \(CN/(\log N)^{1+c}\) for some positive absolute constants \(C\) and \(c\). In particular, this directly implies that the primes contain infinitely many three-term arithmetic progressions, a result originally due to van der Corput, and establishes the first non-trivial case of a conjecture of Erdős on arithmetic progressions. Joint work with Thomas Bloom (University of Cambridge).

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