# The Green-Tao Theorem and a Relative Szemerédi Theorem

Wednesday, October 1, 2014 - 2:00pm - 2:50pm

Keller 3-180

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 every relatively dense subset of a pseudorandom set of integers contains long arithmetic progressions. Our main advance is both a simplification and 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.

One of the main ingredients in the proof is a relative Szemerédi theorem, which says that every relatively dense subset of a pseudorandom set of integers contains long arithmetic progressions. Our main advance is both a simplification and 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.

MSC Code:

11B25

Keywords: