6 problems

Let $K\subseteq\mathbb R^n$ be a convex body, let $X$ be uniformly distributed on $K$, and define the isotropic constant of $K$ by … Let $\Delta^n$ be any simplex in $\mathbb R^n$.…

Strong slicing conjecture. This quantity is maximized among convex bodies with barycenter at the origin by any $n$-simplex whose vertices span $\mathbb{R}^n$ and sum to zero. The c…

Let $G\subset\mathbb{R}^d$ be a convex symmetric body in isotropic position, and let $L(G)$ denote its isotropic constant. Slicing conjecture. There is a constant $C>0$ independent…

KLS implication for the slicing conjecture. If the KLS conjecture holds, then the slicing (hyperplane) conjecture holds.

For a convex body $K\subseteq\mathbb{R}^d$, let $L_K$ denote its isotropic constant. The slicing conjecture. There exists a universal constant $c_3>0$ such that for every dimension…

Let $K,L\subseteq\mathbb{R}^d$ be convex bodies, and let $V_K$ and $V_L$ denote the volumes of the convex hulls of $d+1$ independent random points in $K$ and $L$, respectively. Ass…