School of Mathematical Sciences

Arithmetic progressions in sums of low-density sets menu

Arithmetic progressions in sums of low-density sets

Olof Sisask (QMUL)
Mon, 22/11/2010 - 16:30
Seminar series: 

If A is a subset of the integers {1,...,N} of size alpha*N, how long an arithmetic progression must the sumset A+A = { a + b : a, b in A } contain? This question has been studied by several people, including Bourgain, Ruzsa and Green, who have given good lower and upper bounds for the answer when alpha is roughly at least 1/sqrt(log N). In this talk I shall discuss an approach to finding long arithmetic progressions in A+A when alpha can be as low as roughly 1/log N, with a relatively simple application of the probabilistic method being the main tool. The approach is quite different to previous ones, allowing also for a partial extension to non-commutative groups. Based on joint work with E. Croot.