Mathematics - Colloquium
Friday, November 16, 2012
11:00 AM-12:00 PM
ABSTRACT: How symmetrical should we expect the solution of an optimization problem to be? Some cases lead to striking symmetry (such as crystals), while others are seemingly disordered. In this talk, we'll explore the ground states of systems of classical particles under a radial potential function (for example, the Thomson problem of charged particles on a sphere). These problems arise naturally in physics, information theory, and discrete geometry, and we'll see that many beautiful mathematical objects can be characterized by these sorts of extremal properties. In particular, we'll examine the role played by exceptional mathematical structures in this theory, ranging from the icosahedron to the E_8 root system.
Suggested Audiences: Adult, College
Last Modified: November 8, 2012 at 12:18 PM