McGill University - School of Computer Science

Algorithms Seminar 2003

Everybody is welcome!

DATE: Wednesday, March 19th
TIME: 4:30 PM - 5:30 PM
PLACE: McConnell 320
TITLE: On the Kneser-Poulsen Conjecture for spheres
SPEAKER: Robert Connelly, Mathematics Department, Cornell Univ.

If a finite set of disks in the plane is rearranged so that the distance between each pair of centers does not decrease, then the area of the union does not decrease, and the area of the intersection does not increase. This is the case, in the plane, of a conjecture by Kneser (1955) and Poulsen (1954), recently proved by K. Bezdek and me. The analogous question for disks on the 2-dimensional sphere, and for all higher-dimensional spheres and higher-dimensional Euclidean space remains open. I will show this conjecture for unit spheres for all dimensions, but with the restriction that all the disks on the spheres are hemispheres. This is joint work with K. Bezdek, and follows the same general plan as in the plane, but is somewhat simpler.

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