Thomas Bloom

Control in additive combinatorics and its applications

Bounds for the third moment of the convolution have played an important role recently in additive combinatorics, most notably in the study of the sum-product problem and the growth of convex sets of real numbers. In this talk I will give a unified overview of how and why such third moment bounds are useful in additive combinatorics, including recent advances and further applications to the Balog-Szemeredi-Gowers theorem.