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.