The is a math talk about the best possible sphere packing in 8 dimensions. It was an open problem for many years to show that the best 8-dimensional sphere packing is given by the E8 lattice. We describe the solution to this found by Maryna Viazovska, building on work of Henry Cohn and Noam Elkies.
Typo around 13:40: f(0) and f^(0) should be exchanged in the fractions.
The paper by Henry Cohn and Noam Elkies is arxiv.org/abs/math/0110009
The paper by Maryna Viazovska is at arxiv.org/abs/1603.04246
This talk did not cover the proof that the Leech lattice is optimal in 24 dimensions, but this can be found in arxiv.org/abs/1603.06518
Негізгі бет Sphere packings in 8 dimensions (after Maryna Viazovska)
Пікірлер: 26