The Ricci flow
Dr. C. S. Aravinda
Chennai Mathematical Institute.
14-11-03 (Ricci flow seminar)

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Abstract

The notion of Ricci flow was introduced by R. S. Hamilton in 1982 as a possible approach to solving the classical Poincare conjecture. During the 1980s he proved that under various weak positive curvature assumptions on an initial metric the Ricci flow converges to the metric of a spherical space form. Later he proved the so called Harnack inequality which was crucial in Perelman's analysis of the singularities of the Ricci flow.

In his recent preprints Perelman is supposed to have a proof of the Poincare conjecture using Hamilton's method. The details are still being checked by the experts.

In this seminar we plan to study the early papers of Hamilton. The first two lectures are as follows.