4 problems

Let $\Lambda$ be a Bravais lattice with a decisive layer $C$ whose two points are very asymmetric in the sense described immediately before the conjecture. For $u\in\mathbb R^d$, l…

Triangular-lattice uniqueness conjecture. The triangular lattice $\Lambda_{A_0}$ is the unique solution of $(P)$.

Large-area square-lattice conjecture. If $A$ is sufficiently large, the square lattice is the unique solution of $(P_A)$.

Let a centrally symmetric compound object be packed periodically, and compare its densest Bravais lattice packings with all packings of the object. Conjecture 3. Central symmetry a…