Jerusalem Mathematics Colloquium

Thursday, 3rd April 2008, 4:00 pm
Mathematics Building, Lecture Hall 2

Henry Cohn
(Microsoft Research)

"Universally Optimal Distribution of Points on Spheres"

Abstract: How should one distribute a certain number of points over a sphere, so that they are well separated from each other? One natural method is energy minimization: put an electric charge on each point and let them repel each other. This problem arises naturally in physics, but it extends to far more general spaces and potential functions; it can be viewed as a broad generalization of packing problems. Some of the most remarkable exceptional structures in mathematics (such as the E_8 root system, the Leech lattice minimal vectors, the Schlaefli configuration of 27 points in R^6 related to the 27 lines on a cubic surface, the icosahedron, and the regular 600-cell) are solutions of energy minimization problems of this sort. These examples have a rare property called universal optimality: they simultaneously minimize a broad class of potential functions. This talk will survey what's known and conjectured about universally optimal configurations.

The Jerusalem Mathematics Colloquium is happy to host this year's Erdos lecturer
This is the last of this year's Erdos Lectures in Discrete Mathematics and Theoretical Computer Science (but will be independent of the other lectures). The first two lectures will be held in Math 110
31.03.08 11:00 Fast Matrix Multiplication using Representation Theory
02.04.08 10:30 Mysteries of Euclidean Sphere Packing Bounds

Light refreshments will be served outside the lecture room at 3:30.

List of talks, 2007-08
Archive of talks