Speaker
Description
This talk is based on joint work with Emanuel Milman (Technion) and Hiroshi Tsuji (Institution of Science Tokyo).
The Brascamp–Lieb inequality (for multilinear functionals), originally introduced in 1976 as a generalization of Young’s convolution inequality, has since been found to be useful across a wide range of fields. For example, in 1991, within convex geometry, Ball showed that the Brascamp–Lieb inequality implies the reverse isoperimetric inequality. More recently, it has played a critical role in harmonic analysis, particularly in the context of the Fourier restriction conjecture and the Kakeya conjecture (e.g. Bennett—Carbery—Tao).
In this talk, we focus on inequalities for symmetric convex bodies within convex geometry. Specifically, we consider the Blaschke–Santaló inequality and its multilinear version, a Talagrand-type inequality for the Wasserstein barycenter, the Gaussian correlation inequality and its strengthened version. On the analytic side, we also include a Laplace transform bound and an improvement of Borell’s reverse hypercontractivity.
We will report on new developments obtained by reinterpreting this collection of inequalities from the perspective of the Brascamp–Lieb inequality.