Computation and Optimization of Energy, Packing, and Covering
(April 9 – 13, 2018)
The packing and covering of equal geometric shapes, such as spheres or convex polyhedra, are classical geometric optimization problems. They have a long mathematical tradition and were for instance part of Hilbert's famous twenty-three problems for the 20th century. Nevertheless, seemingly simple packing and covering problems are still extremely hard to solve and generally, far from a solution. Likewise, minimal energy problems for pair potentials, of which best-packing is a special case, have many such unresolved questions.
However, in recent years several new developments with computer assisted approaches have led to previously unexpected breakthrough results. These involve massive computer searches and techniques from numerical optimization, as well as the creation and application of new optimization techniques, such as specific semi-definite programming bounds. New techniques for computer assisted certified proofs allow one to obtain results that would otherwise have been difficult, if not impossible, to check.
During this workshop, we will bring together energy, packing and covering experts from these new computation-based research directions.