Clay Mathematics Institute

Dedicated to increasing and disseminating mathematical knowledge

Ricci Flow, 3-Manifolds and Geometry

June 30 - July 15, 2005

MSRI, Berkeley, CA

Organizers: Gang Tian, John Lott, John Morgan, Bennett Chow, Tobias Colding, Jim Carlson, David Ellwood, Hugo Rossi

Designed for graduate students and mathematicians within five years of their Ph.D., the program is organized around Ricci Flow and the Geometrization of 3–manifolds, particularly, the recent work of Perelman.

The school will consist of three weeks of foundational courses and one week of mini-courses focusing on more advanced topics and applications.

Perelman's work builds on earlier work of Thurston and Hamilton in a deep and original way. The aim of the school is to provide a comprehensive introduction to these exciting areas as well as the recent developments due to Perelman.

Topics covered will include an introduction to Geometrization (3–dimensional geometries, prime decomposition of 3–manifolds, incompressible tori, Thurston's geometrization conjecture on 3–manifolds), Ricci Flow (both geometric and analytic aspects), Minimal Surfaces and various fundamental results in topology and differential geometry used in the work of Perelman.

We will also have a course dedicated to Perelman's work on general Ricci Flow (Entropy functional of Perelman and its local form, Non-collapsing theorem, Perelman's reduced volume and applications), as well as a course that outlines some more advanced results and applications in 3–dimensions (analysis of large curvature part of Ricci flow solutions, Ricci flow with surgery, basic properties of solutions with surgery, long time behavior of solutions, applications to geometrization).