Abstract: I will talk about a joint work with Henry Cohn,
Abhinav Kumar, Stephen D. Miller, and Maryna Viazovska.
We look at the problem of arranging points in Euclidean
space in order to minimize the potential energy. More precisely,
we are interested in cases when a single configuration
is optimal for all potentials that are completely monotone.
Such configurations are called universally optimal.
Until recently the only known example of a universally optimal
configuration in Euclidean space was the 1-dimensional
lattice in R^1. We show that the E8 lattice and the Leech lattice
are universally optimal in dimensions 8 and 24 respectively.
The main ingredient in the proof is an explicit interpolation
formula for Fourier eigenfunctions that is constructed from
(quasi-)modular forms and Eichler integrals for Gamma(2).
Universal optimality of the E8 and Leech lattices
21.05.2019 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: