From Multilinear Kakeya to Additive Energies : Decoupling and Its Use in Combinatorial Number Theory

Abstract: This is a survey of decoupling results in harmonic analysis and their use in combinatorial number theory. The main results are an expository proof of a decoupling inequality for exponential sums in  and a new lower bound on the cardinality of the sumsets of certain convex sequences. There is also some discussion regarding the multilinear Kakeya inequality, the uncertainty principle as well as the use of decoupling in number theory in general.