Universal optimality of the E8 and Leech lattices

Danylo Radchenko (ETH Zürich)

26-Oct-2020, 12:15-13:15 (3 years ago)

Abstract: We look at the problem of arranging points in Euclidean space in order to minimize the potential energy of pairwise interactions. We show that the E8 lattice and the Leech lattice are universally optimal in the sense that they have the lowest energy for all potentials that are given by completely monotone potentials of squared distance. The proof uses a new kind of interpolation formula for Fourier eigenfunctions, which is intimately related to the theory of modular forms. The talk is based on a joint work with Henry Cohn, Abhinav Kumar, Stephen D. Miller, and Maryna Viazovska.

number theory

Audience: researchers in the topic

( slides | video )


Warsaw Number Theory Seminar

Organizers: Jakub Byszewski*, Bartosz Naskręcki, Bidisha Roy, Masha Vlasenko*
*contact for this listing

Export talk to