The Ricci flow, introduced by R. Hamilton in 1982, following earlier work
by Eells and Sampson, deforms a Riemannian metric with a speed given by the
negative of the Ricci tensor. This process often deforms the initial metric
to a canonical metric. For example, a by now classical theorem of Hamilton
asserts that a three-manifold of positive Ricci curvature is deformed to a
spherical space form under the flow.
In this lecture series, I will describe the proof of this result, and discuss to what extent the ideas involved in the proof carry over to higher dimensions. I will begin with a discussion of the evolution of curvature under Ricci flow. Later, I plan to go over a paper by C. Böhm and B. Wilking on manifolds with 2-positive curvature operator. I will also discuss the notion of positive isotropic curvature, and describe my recent joint work with R. Schoen on the Differentiable Sphere Theorem.
Zeit: Mi 10-12
Ort: HG G 43 (Hermann-Weyl-Zimmer)