Mathematics Colloquia and Seminars

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In 1982, Richard Hamilton proposed a program that he believed would lead to a decision in the fate of the Poincare conjecture in three dimensions. This program employed the use of the Ricci flow of the metric of a compact 3-manifold. It wasn't until 2004 when Grigori Perelman used this program to solve the stronger conjecture of Thurston's Geometrization that this program's full utility was seen.

I plan to introduce the Ricci flow of a metric (including some examples), outline Hamilton's proof of concept for his program (showing that closed manifolds admitting strictly positive metrics also admit a constant positive metric), and hint at how the program naturally flows a metric to one of the eight Thurston geometries.