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Past events in this series


Mon, 12 Oct 2026
16:00
C4

Product-free subsets of (0,1) and a strengthened Brunn–Minkowski inequality

Leonardo Franchi
(University of Cambridge (DPMMS))
Abstract
The third problem in Ben Green’s collection of 100 open problems asks whether an open subset of (0,1) containing no x,y,z satisfying xy=z must have measure at most 1/3. In joint work with W. Timothy Gowers and Fredy Yip, we proved this result.
In this talk, I will discuss some of the motivations behind the problem, as well as some of the new tools developed to prove a strengthened version of the one dimensional Brunn–Minkowski inequality that plays a key role in the argument.
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