Sphere Packings and Lattices
Densest packings, kissing numbers, and Viazovska's E8 / Leech results.
Sphere Packings and Lattices. Densest packings, kissing numbers, and Viazovska’s E8 / Leech results.
Foundations and canonical references
The standard treatments of sphere packings and lattices approach the subject from complementary angles. Conway, Sphere Packings, Lattices and Groups (1999) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Supporting and adjacent work
A number of supporting contributions sharpen specific aspects of sphere packings and lattices or connect it to neighbouring problems. The sphere packing problem in dimension 8 (Viazovska, 2017) contributes to this area as one of the supporting references that inform current practice.
Open methodological questions for sphere packings and lattices include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1999Sphere Packings, Lattices and Groupsconway-1999, sloane-1999
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