3 problems

Let $f$ be the Lennard–Jones-type interaction defined by … where $(a_1,a_2)\in(0,+\infty)^2$ and $0<x_1<x_2$. Let $E_f$ denote the interaction energy among Bravais lattices, and le…

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…

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…