ResearchResearch preprint
High-Dimensional Sphere Packing
From a simple question and an AI-directed search to a collaborative preprint on lattice packing in every sufficiently large dimension.
Mathematical papers
Work in mathematics and computational geometry.
Explore the 2 articles ↓This collection brings together my mathematical writing, including work in computational geometry. Each article identifies its status: a public preprint, an unpublished manuscript, or a research note.
Sphere packing drew my attention because the problem is easy to explain, even in high dimensions, while the mathematics behind it is complex. I first tried small-dimensional kissing problems, then moved toward mathematical results in large dimensions.
The sphere-packing article follows that path through AI-assisted exploration and collaboration with Nihar Gargava and Matthias Gröbner. Our preprint gives a lattice-packing lower bound in every sufficiently large dimension.
My earlier work in computational geometry includes an unpublished manuscript on convex hulls with limited working memory.
Subtopics
Articles in this topic
2 articles
ResearchResearch note
Convex hulls with limited working memory
Batched bridge searches for read-only point sets: a current manuscript developing a methodology I recall working on around 2009.