Gaps between primes in Beatty sequences

Abstract: 

We will present a some results on the gaps between primes in Beatty sequences, sequences of the form [αn+β][αn+β] with αα irrational and ββ real.  The results follow from a general theorem on the gaps between primes in sets that satisfy certain regularity conditions.  The methods follow the recent breakthrough of J. Maynard. This is joint work with R. C. Baker.