3/24/2004

Timothy Gowers
Cambridge University

Szemeredi's regularity lemma is a major tool in graph theory. Recently, it and a companion result have been generalized to hypergraphs, and a consequence of these developments is the first proof of the multidimensional Szemeredi theorem that does not rely on Furstenberg's ergodic-theoretic techniques, and the first to give an explicit (though very weak) bound.