Product-free subsets of [0, 1].

Speaker: Fredy Yip (Cambridge)
Series: Combinatorics Seminar
Note: Note non standard day for talk

Abstract: The Brunn-Minkowski inequality on R asserts that |A + B| >= |A| + |B| for (open) subsets A and B of R where equality holds precisely when A and B are intervals. We show that this inequality may be significantly strengthened when A and B are far from being intervals in a suitable sense, giving a stability version of the inequality which is tight across a variety of different regimes of interest. Our methods are motivated by and lead to a resolution of the third problem on Ben Green’s list of 100 problems, which concerns the maximal measure of a product-free subset of [0, 1].

Joint work with Leonardo Franchi and Timothy Gowers.