Julian Sahasrabudhe

On Combinatorial discrepancy and an old problem of J.E. Littlewood

Given a collection of sets A1,...,Am ⊆ [n], the basic problem in combinatorial discrepancy theory is to find a colouring of [n] with {+1,-1} so that, for each i ∈ [m], the sum of f over the elements A_i is as small in absolute value as possible. In this talk, I will discuss how the sort of combinatorial and probabilistic reasoning used to think about problems in combinatorial discrepancy can be adapted to solve an old conjecture of J.E. Littlewood in harmonic analysis.