Title:  The Graph Removal Lemma

Speaker:  Jacob Fox, MIT

Abstract:

Let H be a fixed graph with h vertices. The graph removal lemma states that
 every graph on n vertices with o(n^h) copies of H can be made H-free by
 removing o(n^2) edges. It has many applications in theoretical computer
 science, extremal graph theory, additive combinatorics, and discrete
 geometry. We give a new proof of the graph removal lemma which avoids
 Szemeredi's regularity lemma and gives a better bound. This approach also
 works to give improved bounds for the directed and multicolored analogues of
 the graph removal lemma. This answers questions of Alon and Gowers.