3 problems

Let $K\subseteq\mathbb{R}^n$ be centrally symmetric, let $K^\circ$ be its polar body, and let $(\vec{x},\vec{y})$ be uniformly distributed on $K\times K^\circ$. Polar second-moment…

Let $L_f$, $\widetilde{L}_f$, and $\widehat{L}_f$ be the three functional isotropic constants defined for integrable centered log-concave functions. Define … Functional strong slic…

Bourgain's slicing conjecture. There exists a constant $c>0$ independent of dimension such that