Panagiotis Gianniotis, Department of Pure Mathematics, University of Waterloo
“The Ricci flow on 3-manifolds with positive Ricci curvature”
Ricci flow is a geometric evolution equation, introduced by Hamilton in 1982. By analogy to heat diffusion, Ricci flow is meant to deform a given Riemannian metric on a manifold to a canonical metric, namely one that has the maximal amount of symmetry. Canonical metrics then reveal information about the topology of the manifold. In particular, Hamilton used Ricci flow to prove that any 3-manifold admitting a metric with positive Ricci curvature should be diffeomorphic to a quotient of the 3-sphere, and Perelman used it to prove Thurston’s Geometrization conjecture, with the Poincare conjecture following as a corollary.
In this talk, I will describe a proof of Hamilton’s result, and use it as an opportunity to present some of the key ideas behind the study of Ricci flow.
MC 5403