5 problems

Minimality for $\textnormal{E}_{\textnormal{BPD}}$ in general. For all $N\in\mathbb N\backslash\{0,1\}$, we have

Let $E_f(L)$ denote the lattice energy of a two-dimensional lattice $L$, and consider the potential $f(r)=e^{-\beta\pi r}-e^{-\alpha\pi r}$, where $\alpha$ and $\beta$ are paramete…

Let $L$ be a two-dimensional lattice of area $A$, and let $E_f(L)$ denote its lattice energy for a potential $f$. A potential is completely monotone if it satisfies…

Let $r_0>0$. For a Bravais lattice $L$ in dimension $3$, let $E_{\alpha,r_0}[L]$ denote the Morse lattice energy, let $\mathcal{L}_3$ be the class of Bravais lattices, and let…

Common-neighbor conjecture. If $z,z'\in Z$ satisfy \\#N(z)=\\#N(z')=12 and $z\in N(z')$, then