6 problems

Plan–Vershynin conjecture. A dependence of order $\delta^{-2}$ times the square of the Gaussian width should be necessary and sufficient for a random hyperplane tessellation on the…

Let $T\subseteq\mathbb{R}^n$ be a set of adversarial tricks, let $X$ have the standard normal distribution in $\mathbb{R}^n$, and let the corrupted observation be $X+rt$, where…

Let $\boldsymbol{x}$ and $\boldsymbol{\Sigma}$ denote the objects defining the functional Gaussian width $\mathcal{G}(\boldsymbol{x},\boldsymbol{\Sigma})$ and the standard Gaussian…

Polylogarithmic convex-hull conjecture. For every fixed $k \ge 4$, one can choose an admissible set $S$ satisfying

Small convex-hull conjecture. The bound on the size of such a set $S$ can be improved to $e^{N^{o(1)}}$.

Gaussian-width conjecture. For any fixed $k \ge 4$,