Jacob Fox: Ramsey numbers
For a graph H, the Ramsey number r(H) is the minimum number N such
that every 2-coloring of the edges of the complete graph contains a
monochromatic copy of H. In these lectures, I will discuss some of the
major results and problems on estimating Ramsey numbers of graphs and
hypergraphs, and some of the methods that have been used to study
them, including the stepping-up technique, regularity method, greedy
embedding strategy, and dependent random choice.
Time permitting, we will also discuss Ramsey numbers of words.