3 papers
math.MG2026
Improved kissing numbers in seventeen through twenty-one dimensions
Henry Cohn, Anqi Li
We prove that the kissing numbers in 17, 18, 19, 20, and 21 dimensions are at least 5730, 7654, 11692, 19448, and 29768, respectively. The previous records were set by Leech in 196…
math.MG2026
Variations on five-dimensional sphere packings
Henry Cohn, Isaac Rajagopal
We analyze SzöllÅsi's recent construction of a conjecturally optimal five-dimensional kissing configuration and produce a new such configuration, the fourth to be discovered. We…
math.MG2024
From sphere packing to Fourier interpolation
Henry Cohn
Viazovska's solution of the sphere packing problem in eight dimensions is based on a remarkable construction of certain special functions using modular forms. Great mathematics has…