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Graduate Organized Seminar - Partitions of the Sphere

Christopher Cox, Department of Mathematics, Washington University in St. Louis

June 27, 2012 - 4:00 pm to 5:00 pm
Location: Cupples I, Room 6 | Host: Timothy Chumley

Abstract: The spherical partition problem asks for the least-perimeter partition of S2 enclosing a specified number of regions of given area. Historically, solutions required added hypotheses such as convexity or the requirement that the regions be connected, but in the last twenty years several general cases have been solved. We will look at the disparate methods by which Hales proved the dodecahedral case and Engelstein proved the tetrahedral case, and consider the open problem of six equal-area regions.

 

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