George Shakan

An analytic approach to Sumsets

Let U be a subset of Z^d. The quantity |U+U|/|U|, known as the doubling constant, has been extensively studied in additive combinatorics. We replace this with a more complicated notion which enjoys a certain tensorisation property. As a result we obtain a new method for studying high dimensional sumsets analogous to the Prékopa-Leindler inequality. We outline some of the main results, key ideas and applications. This is joint work with Dávid Matolcsi, Imre Ruzsa and Dmitry Zhelezov.