# Jerusalem Mathematics Colloquium

Thursday, 3rd April 2008, 4:00 pm

Mathematics Building, Lecture Hall 2

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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