Optimal sphere packing in dimensions 8 and 24
Empaquetamiento óptimo de esferas en dimensiones 8 y 24
- Date
- 2016 · confidence high
- Place
- Berlin (Humboldt University), Germany
- Credited to
- Maryna Viazovska (dimension 8); with Cohn, Kumar, Miller and Radchenko (dimension 24)
- People
- 👤 Abhinav Kumar1984–👤 Danylo Radchenko👤 Henry Cohn👤 Maryna Viazovska1984–👤 Stephen D. Miller
- Field
- Knowledge & symbols
What was discovered
The E8 lattice and the Leech lattice are the densest packings of their dimensions, proved using an auxiliary function built from modular forms. A 23-page proof, compared with Hales's 300 pages in dimension 3.
Viazovska received the Fields Medal in 2022, the second woman to do so.
What it led to
- modular forms in optimisation
- cryptographic codes and lattices
- the universality of E8 and Leech as energy minimisers (2019)
Built on
- Kepler conjecture (Hales)
- Cohn and Elkies's linear programming bounds (2003)
- Leech lattice (1967)
Made possible
- design of error-correcting codes