5 problems

Lagarias' periodicity conjecture. If an FQ has Delone support $K$ and Delone spectrum $\widehat{K}$, then it is periodic.

Lower-bound conjecture. The point count satisfies

A Fourier quasicrystal on $\mathbb R^n$ is a multiset whose associated measure and Fourier transform are both discrete measures. In dimension one, Olevskii and Ulanovskii character…

Let $\mu$ be a crystalline measure on $\mathbb R^n$ with support $\Lambda$ and spectrum $S$. A set is relatively uniformly discrete if it is a finite union of uniformly discrete se…

Lagarias's conjecture. If $\Lambda$ and $S$ are uniformly discrete, then $\mu$ is trivial and all the lattices $L_j$ are equal. The conjecture is known when $n=1$ or when $\mu$ is…