Mon, December 2, 2019
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4:00pm [4:00pm] Danylo Radchenko: ETH Zurich: Colloquium via videoconference
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.
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