5 problems

Triangular lattice minimizer conjecture. For every $s>2$, the triangular lattice $\mathsf{A}_2$ is the unique minimizer of $\mathcal{F}_s$ among all two-dimensional lattices of uni…

A periodic lattice is a discrete subgroup of Euclidean space whose quotient is compact. The crystallization conjecture. Most ground states of physical interacting systems, especial…

Let $\mathcal{C}\subset\mathbb{R}^2$ be an infinite point configuration with unit density, and let $f$ be completely monotone with $|f(r)|=O(r^{-1-\varepsilon})$ as $r\to\infty$ fo…

Let $\mathcal{C}\subset\mathbb{R}^2$ be an infinite point configuration with density … where $B_R$ is the ball of radius $R$ centered at $0$. Let $f$ be completely monotone and sat…

Universal optimality conjecture. For all $N\in2\mathbb{N}$, $\mathsf{A}_2$, $\mathsf{E}_8$, and the Leech lattice are the unique maximizers of $E_f^\pm$ on $\mathcal{A}_N^1$ in the…