George Shakan

Oxford University

An analytic approach to Sumsets

Combinatorics Seminar

24th November 2020, 11:00 am – 12:00 pm
Virtual (online) Zoom seminar; a link will be sent to the Bristol Combinatorics Seminar and Bristol Number Theory Seminar mailing lists, the week before the seminar.

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.

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