The 2003 Annual Meeting of the Clay Mathematics Institute was hosted by MIT at the MIT Media Lab in the afternoon of November 14. The meeting opened with remarks by president Jim Carlson and presentation of the Clay Research Awards. Following the presentation were talks by Richard Hamilton on Ricci Flow and by John Morgan on Ricci Flow, Perelman's work, and the Poincaré Conjecture.
The recipients of the awards were Richard Hamilton of Columbia University and Terence Tao of UCLA. Awardees receive a sculpture by artist Helaman Ferguson and appointment as a Clay Research Scholar.
Richard Hamilton was recognized for his profound contributions to topology, geometry, and analysis through his discovery and development of the Ricci Flow Equation. The Ricci flow equation is much like the classical heat equation except that (a) it is a system of equations, (b) it is nonlinear, and (c) the quantity that evolves is not temperature, but the metric. Thus the Ricci Flow Equation governs the evolution of the geometry of a manifold.
Conceived as a tool for proving both the Poincaré Conjecture and Thurston's Geometrization Conjecture, Hamilton's first success was with positively curved three-manifolds. He proved that any simply connected three-manifold with positive Ricci curvature evolves to a state of constant curvature and thus is the standard three-sphere.