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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


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).

Zoom Notes: The Meeting ID and Passcode will be recurring and should work every Wednesday. The password has been sent out on the department mailing lists. Please email Wushi Goldring   if you are not on these mailing lists and are interested in attending.