Coloring the Voronoi Tessellation of Lattices
summary
The talk studies coloring the Voronoi tessellation of Euclidean lattices: assigning colors to Voronoi cells so adjacent cells differ. It focuses on algorithmic and geometric aspects for lattices, using computational methods and lattice theory to determine colorings and chromatic numbers for specific lattices and to analyze constraints coming from lattice symmetries and Voronoi cell geometry.
AI-written summary · about
chapters (10)
- 0:00Intro
- 1:52Problem statement: Coloring lattices
- 4:51Generalities on chromatic numbers
- 5:51Satisfiability for testing coloring
- 9:15Spectral lower bounds
- 13:09Empty sphere and Delaunay polytopes
- 21:32Hoffman lower bounds for lattices
- 23:01Hoffman lower bounds for root lattices
- 36:21Three-dimensional case
- 37:27Exponential growth