7 problems

Let … be the hexagonal lattice. A lattice is universally optimal if it minimizes every admissible energy among configurations of the same density. Cohn–Kumar's conjecture. The line…

A configuration $\mathcal P$ is universally optimal if it minimizes energy for every sufficiently rapidly decreasing potential $\varphi$ that is completely monotonic as a function…

Let $A_2$ denote the hexagonal lattice, normalized to have point density $1$. A point configuration is universally optimal if it minimizes potential energy among all configurations…

Consider the two spherical codes in the source having respectively $40$ points in $\mathbb{R}^{10}$ and $64$ points in $\mathbb{R}^{14}$. Universal-optimality conjecture. These two…

For $\beta>0$, let … and, for $m\geq 2$, define … A configuration is $L^m_\beta$-universally optimal if it minimizes every admissible periodic energy among $2m$-point configuration…

Let $\mathcal C$ be the code constructed in the paper consisting of $85$ points in $\mathbb C^5$, viewed projectively. A code is universally optimal if it minimizes every admissibl…

In two dimensions, consider the linear programming bounds for energy minimization and the hexagonal lattice. Cohn–Kumar sharpness conjecture. The linear programming bounds should b…