Combinatorial discrepancy and a problem of J.E. Littlewood

Given a collection of subsets of a set X, the basic problem in combinatorial discrepancy theory is to find an assignment of 1,-1 to the elements of X so that the sums over each of the given sets is as small as possible. I will discuss how the sort of combinatorial reasoning used to think about problems in combinatorial discrepancy can be used to solve an old conjecture of J.E. Littlewood on the existence of ``flat Littlewood polynomials''.

This talk is based on joint work with Paul Balister, Bela Bollobas, Rob Morris and Marius Tiba.