Frank Vallentin: Chromatic numbers of geometric graphs

Abstract: A classical problem in discrete geometry (due to Hadwiger and Nelson) is to find the minimal number of colors one needs to color all points in the Euclidean plane so that no two points which are distance 1 apart receive the same color. Similar geometric coloring problems can be posed in the context of the hyperbolic plane, n-dimensional Euclidean spaces, n-dimensional spheres, or coloring the Voronoi tessellation of n-dimensional lattices. In this talk I will present a theoretical framework in which all these geometric coloring problems (assuming that the color classes are measurable sets) can be conveniently studied with the help of harmonic analysis and convex optimization.