Primes in arithmetic progressions to smooth moduli

Zhang (2013) proved that there exists some h such that n and n+h are both prime for infinitely many choices of n. In this talk I will sketch which role equidistribution estimates for primes in APs to smooth moduli play in Zhang's proof. Relatedly, Polymath (2014) showed that the primes have exponent of distribution 1/2+7/300 to smooth moduli. I will briefly indicate how an alternative version of the q-van der Corput method can be used to improve on this exponent.