Algebraic Structures in the Reinhardt Problem

A problem in discrete geometry, called the Reinhardt problem, is (roughly speaking) to determine the shape of the convex disk in the plane that is the most unpackable. A shape is highly packable if copies of it can fill the plane with high density. A square is highly packable. The circle is relatively unpackable.

This talk will describe some of the structures in algebra and geometry that are needed for this problem. Some of the topics to be touched on are Lie groups, Lie algebras, models of non-Euclidean geometry, symplectic geometry, bundles, a generalization of Noether's theorem, and valued fields.