Wikinventia — Atlas of discoveries and inventions · Digital Age

Optimal sphere packing in dimension 8 — Maryna Viazovska

2016 AD · Transmission: Global
MathematicsTheorySlavic

Maryna Viazovska solves, in a preprint published on March 14, 2016, the optimal sphere-packing problem in dimension 8, proving that the E8 lattice provides the densest possible arrangement of identical spheres in that space — a problem that had been open for decades. A few weeks later, together with several collaborators, she extends the method to dimension 24 using the Leech lattice. The technique employed, based on special modular functions, proves surprisingly direct compared with previous approaches that had failed for years in dimensions higher than 3. Viazovska received the Fields Medal in 2022, the second woman, after Maryam Mirzakhani, to receive it.

InstitutionÉcole Polytechnique Fédérale de Lausanne
Historical regionUkraine / Switzerland
Primary sourceViazovska, M. — "The sphere packing problem in dimension 8" (Annals of Mathematics, 185, 2017, preprint from March 14, 2016). DOI: 10.48550/arXiv.1603.04246
Secondary sourceInternational Mathematical Union — Fields Medal citation 2022
Original languageEnglish
View this entry in the interactive atlas →