Geometry Forum
Friday, October 9, 2009, 1:15pm, 205 Physics
Graham Cox (Duke University)
The entropy formula for the Ricci flow and its geometric applications
Abstract:
This talk will cover the first 4 sections of Perelman's paper "The entropy formula for the Ricci flow..." After some preliminary definitions and examples, I will demonstrate how Ricci flow can be realized as a gradient flow in an appropriate space of metrics. The resulting monotone quantities will then be used to show that periodic solutions (breathers) are in fact fixed points (gradient solitons) of the flow. Finally, I will discuss the celebrated "no local collapsing" theorem and some of its applications to the study of finite-time singularities.

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