Carlo Vanoni

Analysis of Conjectural Improvements to Minkowski's Lower Bound on the Sphere Packing Density

Torquato and Stillinger conjectured an exponential improvement of Minkowski's classical lower bound on the maximal density of sphere packings in high-dimensional Euclidean space $\mathbb{R}^d$ using a pair-correlation-function optimization framework. Conditional on their realizability conjecture, we show that a simple...