Abstract: It was only recently that the well-known conjecture that the primes contain arbitrary long arithmetic progressions had been finally proved. The result is due to Ben Green and Terence Tao. I shall briefly try to explain how ergodic-theoretic proof techniques like Furstenberg's Multiple Ergodic Theorem and Gowers norms were applied there.
The talk is meant to be just a resume of an article by Bryna Kra, Bull. AMS 43 (p. 3-23).