6 problems

Consider complex and quaternionic convex bodies, meaning unit balls of complex and quaternionic norms. The complex or quaternionic $\ell^1$ and $\ell^\infty$ unit balls are respect…

Let $K\subseteq\mathbb{R}^n$ be a centrally symmetric convex body, with associated bottleneck domain $K^\diamondsuit\subseteq K\times K^\circ$. Bottleneck-product uniqueness conjec…

Let $K\subseteq\mathbb{R}^n$ be a centrally symmetric convex body, let $K^\circ$ be its polar body, and let $K^\diamondsuit\subseteq K\times K^\circ$ be the associated bottleneck d…

Simplex asymptotic conjecture.

Uniqueness conjecture for $L^p$-Mahler minimizers. Up to the action of $GL(n,\mathbb{R})$, $\mathcal{M}_p$ is uniquely minimized by the cube among symmetric convex bodies, and by t…

Existence conjecture. There is a symmetric convex set $K$ in $\mathbb{R}^n$ such that