Abstract
This lecture began with a discussion of the " corner theorem ", according to which a dense subset of the n-grid × n must contain a triplet of points of the form(x,y),(x,y + d) and(x + d,y). This theorem is linked to several other results, including a statement on configurations in linear 3-uniform hypergraphs. To prove this statement, a very useful tool is Szemerédi's regularity lemma, which states that any graph can be divided into a small number of quasi-random parts.
