Manchester Building (Hall 2), Hebrew University Jerusalem
A very old question in additive number theory is: how large can a subset of Z/NZ be which contains no three-term arithmetic progression? An only slightly younger problem is: how large can a subset of (Z/3Z)^n be which contains no three-term arithmetic progression? The second problem was essentially solved in 2016, by the combined work of a large group of researchers around the world, touched off by a brilliantly simple new idea of Croot, Lev, and Pach. It turns out that this is yet another example where the so-called “polynomial method” gives a very short solution to an old and seemingly difficult problem in combinatorics. I’ll explain the proof and talk about some of the many interesting research directions that have been touched off by the new developments.