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Thursday, March 29, 2018

**Abstract:** Vinogradov showed in 1937 that every large enough odd integer can be represented as a sum of three primes. One may ask what if these primes are restricted to some (potentially sparse) subset of the primes. In general, if the set is badly distributed in congruence classes or Bohr sets, the result does not necessarily hold. In this talk I will describe two "transference type'' results aimed to show the obstructions described above are the only obstructions. As applications, we get that Vinogradov's three primes theorem holds for Chen primes and for primes in short intervals. This is based on joint works with K. Matomaki and J. Maynard.