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370. The sphere packing problem on Tori
Invited abstract in session WA-38: Recent advances in LP and SDP for discrete optimization problems, stream Conic Optimization: Theory, Algorithms, and Applications.
Wednesday, 8:30-10:00Room: 34 (building: 306)
Authors (first author is the speaker)
| 1. | Andreas Spomer
|
| University of Cologne |
Abstract
How can we arrange spheres in a way such that they fill out as much space as possible? This age-old mathematical question has a lot of applications, not only in mathematics, but also in physics and other areas of natural science. The problem has been studied in many interesting spaces, for example in finite fields, on the sphere and in the Euclidean space. In recent times, a lot of progress has been made, for example by the winner of the Fields medal Maryna Viazovska, who solved the problem in the eight dimensional Euclidean space.
In my talk, I want to consider this problem on spaces that are given by the Cartesian product of spheres. We will look at a family of dense packings and discuss how to verify their optimality using semidefinite programming, harmonic analysis and sum-of-squares techniques. Furthermore, we will relate this problem to other packing problems in different spaces.
Keywords
- Programming, Semidefinite
Status: accepted
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