Arithmetic Progressions in Primes

Arithmetic Progressions in Primes - Madhur Tulsiani

Madhur Tulsiani
Institute for Advanced Study
November 24, 2009

I will discuss the Green-Tao proof for existence of arbitrarily long arithmetic progressions in the primes. The focus will primarily be on the parts of the proof which are related to notions in complexity theory. In particular, I will try to describe in detail how the proof can be seen as applying Szemeredi's theorem to primes, by arguing that they are indistinguishable from dense subsets of integers, for a suitable family of distinguishers.