Description
IITB Mathematics Colloquium via videoconference.
Speaker: Danylo Radchenko.
Affiliation: ETH Zurich.
Date and Time: Monday 02 December, 4:00 pm - 5:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Universal optimality of the E8 and Leech lattices.
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.