Alexei Andreanov (Institute for Basic Science, Korea)
Abstract. Sphere packing is an old (optimization) problem at the intersection of mathematics, physics, and computer science. The formulation of the problem is very simple — what is the densest arrangement of spheres in a given Euclidean dimension. Despite that, the solution proved to be very hard to find, even approximately. The proofs for d=2,3 were only established in 20th century, while in higher dimensions our knowledge remains limited despite over a hundred years of research. The complexity of the problem originates from the combinatorial optimization nature and the failure of our intuition in high dimensions. While there is a large body of results from (pure) mathematics, I am going to present some new results in lattice sphere packing based on a theory by Voronoi and methods of statistical mechanics. I will also discuss the decorrelation principle, a recent conjecture, that has important immplications for the problem of packing.