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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Song of the Week: The Blow Monkeys - It Doesn't Have to Be This Way

Dr Robert, leader of the Blow Monkeys, took his name from a Beatles song. The comparison with the Fab Four ends there, but this is also fab.

You may think it sounds a like a pop/soul love song, but in fact it is a critique of the socio-economic conditions in Britain at the time.

New books

If you have published a book recently, whatever the topic, whether maths or even romantasy, please let Dyrol know as we like to feature them in the Bulletin and in the display cabinets in the mezzanine.

Here's David Acheson's latest

Classical simulation of circuits with realistic odd-dimensional Gottesman-Kitaev-Preskill states
 Calcluth, C Hahn, O Bermejo-Vega, J Ferraro, A Ferrini, G (17 Dec 2024) https://arxiv.org/abs/2412.13136v2
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