Speaker : Professor Neal Bez, Saitama University

Title : The Brascamp-Lieb Inequality

Abstract:

The Brascamp-Lieb inequality is a powerful and far-reaching generalisation of Holder’s
inequality, Young’s convolution inequality and the Loomis-Whitney inequality. In this
talk I will introduce various fundamental results on the Brascamp-Lieb inequality, in-
cluding Lieb’s theorem on near-maximizers and a characterization of the feasibility of the
inequality due to Bennett, Carbery, Christ and Tao. I will also explain the important
role of the so-called geometric Brascamp-Lieb inequality and how one can prove this case
in an elegant way using the heat equation. In the remaining time, I will mention recent
developments on the inverse form of the Brascamp-Lieb inequality.

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