5 problems

Let $A\in\mathbb{R}^{m\times d}$, with rows denoted by $A_i$, and define … Here $\gamma_m$ denotes standard Gaussian measure on $\mathbb{R}^m$. $\ell_1$ partial-coloring conjecture…

Let $A\in\mathbb{R}^{m\times d}$ with $m\geq d$ and $0<\varepsilon\leq\frac12$. Sparse $\ell_1$ representation conjecture. There exists a universal constant $C>0$ and a matrix…

Let a preference profile on four candidates be ell-1-Euclidean if it is realizable by candidate positions and voter ideal points in the plane, with preferences determined by the el…

Let $A$ be a compact $\ell_1$-convex set, meaning a geodesic subset of $\ell_1^n$, and let $V'_i(A)$ denote its $i$th $\ell_1$-intrinsic volume. These volumes are defined by the St…

Let $n$ be the number of points in a finite semi-metric space. The minimum $\ell_1$-dimension is the smallest integer $d$ such that every isometrically $\ell_1$-embeddable semi-met…