Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

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The Kepler conjecture
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**
Thomas C. Hales , University of Michigan**

This talk describes two theorems in discrete geometry. The first is the proof of the Kepler conjecture. The Kepler conjecture asserts that the densest packing of equal spheres is achieved by the face-centered cubic packing. The second is a proof of the honeycomb conjecture. The honeycomb conjecture asserts that the optimal partition of the plane into cells of equal area is the regular hexagonal tiling.

Both of these problems are limiting cases of a general foam problem that has been proposed by Phelan and Weaire. The dry foam limit is the honeycomb conjecture in two dimensions and the Kelvin problem in three. The wet foam limit is the sphere packing problem.

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