### Rutgers Discrete Mathematics Seminar

Title: The Green-Tao theorem and a relative Szemerédi theorem

Speaker: **Yufei Zhao**, MIT

Date: Tuesday, November 12, 2013 2:00pm

Location: Hill Center, Room 525, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:
The celebrated Green-Tao theorem states that there are arbitrarily long arithmetic progressions in the primes. In this talk, I will explain the ideas of the proof and discuss our recent simplifications. One of the main ingredients in the proof is a relative Szemerédi theorem, which says that any subset of a pseudorandom set of integers of positive relative density contains long arithmetic progressions. Our main advance is a simple proof of a strengthening of the relative Szemerédi theorem, showing that a much weaker pseudorandomness condition suffices. Based on joint work with David Conlon and Jacob Fox.

See: http://math.rutgers.edu/seminars/allseminars.php?sem_name=Discrete%20Math