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Minor Oral, Geometry & Topology Seminar - Length Minimizing Partitions of the Sphere

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

October 4, 2013 - 3:00 pm to 4:00 pm
Location: Cupples I, Room 199 | Hosts: Profs. Renato Feres & Xiang Tang

Abstract: The spherical partition problem seeks a length minimizing partition of the sphere S² into N not necessarily connected regions. In 2002, Thomas Hales adapted a key idea from his proof of the Honeycomb Conjecture to solve the N=12 case, showing the dodecahedral partition is optimal. In 2010, Max Engelstein solved the N=4 case, proving that the tetrahedral case was best. It remains open whether the cubic partition is length minimizing for six regions.