114 citations · 1k across the 63 of their papers we have counts for
6 papers · 1 filter
The Green-Tao theorem: an exposition
David Conlon, Jacob Fox, Yufei Zhao
The celebrated Green-Tao theorem states that the prime numbers contain arbitrarily long arithmetic progressions. We give an exposition of the proof, incorporating several simplific…
An arithmetic transference proof of a relative Szemerédi theorem
Yufei Zhao
Recently Conlon, Fox, and the author gave a new proof of a relative Szemerédi theorem, which was the main novel ingredient in the proof of the celebrated Green-Tao theorem that the…
A short proof of the multidimensional Szemerédi theorem in the primes
Jacob Fox, Yufei Zhao
Tao conjectured that every dense subset of , the -tuples of primes, contains constellations of any given shape. This was very recently proved by Cook, Magyar, and…
Linear forms from the Gowers uniformity norm
David Conlon, Jacob Fox, Yufei Zhao
This is a companion note to our paper 'A relative Szemerédi theorem', elaborating on a concluding remark. In that paper, we showed how to prove a relative Szemerédi theorem for $(r…
A relative Szemerédi theorem
David Conlon, Jacob Fox, Yufei Zhao
The celebrated Green-Tao theorem states that there are arbitrarily long arithmetic progressions in the primes. One of the main ingredients in their proof is a relative Szemerédi th…
Sets Characterized by Missing Sums and Differences
Yufei Zhao
A more sums than differences (MSTD) set is a finite subset S of the integers such |S+S| > |S-S|. We show that the probability that a uniform random subset of {0, 1, ..., n} is an M…