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Defining optimal packings and coverings with the aid of topology


Speaker: Greg Kuperberg, UC Davis Mathematics
Location: 593 Kerr
Start time: Tue, Oct 24 2000, 2:00PM

What is the best way to pack congruent copies of some shape in n-dimensional Euclidean space? This important question in geometry presupposes that there is a rigorous notion of what it means for a packing to be "best". Certainly a best packing should have maximum density, but this condition is not enough. Defining optimality of packings (and coverings) is a subtle matter, and I will discuss how ideas from topology, dynamical systems, and measure theory help clarify it.