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Defining optimal packings and coverings with the aid of topology
Geometry/Topology| Speaker: | Greg Kuperberg, UC Davis Mathematics |
| Location: | 593 Kerr |
| Start time: | Tue, Oct 24 2000, 2:00PM |
Description
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.