4 problems

Let $N$ be a Fibonacci number, let the Fibonacci lattice be the corresponding lattice point configuration on the torus, and let $f$ be a potential in the broad class of potentials…

Modified Fibonacci lattice dispersion conjecture. We conjecture that this dispersion formula holds for all $m\geq 5$. Numerical computations for $m\in\{5,6,7,8,9,10\}$ support the…

Let ${{\mathcal P}_{n}}\subset [0,1]^2$ be a point set with $n$ points, and let $\operatorname{disp}({{\mathcal P}_{n}})$ denote the area of the largest rectangle in the two-dimens…

Global optimality conjecture. For $n=F_m$, the Fibonacci lattice is globally optimal for periodic $L_2$-discrepancy among all point sets with $n$ points.