Online: Linear equations in subsets of the primes

Zoom Online Meeting ID: 919 6497 4060
For password see the email or contact Pieter Moree (moree@mpim...).

The Green-Tao theorem states that the set of primes contain arbitrarily
long arithmetic progressions. It is reasonable to wonder whether the
same holds for certain subsets of the primes, and also whether
arithmetic progressions may be replaced by other linear configurations,
i.e. solutions to systems of linear equations. I will review known
results in that area, and talk about an ongoing work with Joni
Teräväinen and Fernando Shao, where we provide a general criterion for a
set of integers to contain linear configurations, and show that this
criterion applies to certain interesting sets of primes such as Chen
primes or almost twin primes.