Jacob Fox

Szemerédi's regularity lemma and its variants are some of the most powerful tools in combinatorics. For example, Szemerédi used an early version in the proof of his celebrated theorem on long arithmetic progressions in dense sets of integers. It has...

A graph is Ramsey if its largest clique or independent set is of size logarithmic in the number of vertices. While almost all graphs are Ramsey, there is still no known explicit construction of Ramsey graphs. We discuss recent progress on finding...