|Computer Science/Discrete Mathematics Seminar I|
|Topic:||The Green-Tao theorem and a relative Szemeredi theorem|
|Affiliation:||Massachusetts Institute of Technology|
|Date:||Monday, March 3|
|Time/Room:||11:15am - 12:15pm/S-101|
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.