The Green-Tao theorem and a relative Szemeredi theorem

Computer Science/Discrete Mathematics Seminar I
Topic:The Green-Tao theorem and a relative Szemeredi theorem
Speaker:Yufei Zhao
Affiliation:Massachusetts Institute of Technology
Date:Monday, March 3
Time/Room:11:15am - 12:15pm/S-101
Video Link:https://video.ias.edu/csdm/2014/0303-YufeiZhao

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 Szemeredi theorem, which says that any subset of a pseudorandom set of integers of positive relative density contains long arithmetic progressions. Our main advance is both a simplification and a strengthening of the relative Szemeredi theorem, showing that a much weaker pseudorandomness condition suffices. I will explain the transference principle strategy used in the proof. Based on joint work with David Conlon and Jacob Fox.