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Stability problems and singularities of the Ricci flow

JunProf. Dr. Klaus Kröncke

Mittwoch, 2020-10-21 11:30Uhr

The Ricci flow is a geometric evolution equation for Riemannian metrics on a manifold, which is of fundamental importance in modern Riemannian geometry. Generally, its solutions may develop singularities after finite time. Such a singularity always admits a blowup limit, which is a self-similar solution of the Ricci flow, also called a Ricci soliton. In this talk, I will give a review on stability results for Ricci solitons under the Ricci flow in different geometric situations, with specific attention given to recent results in the asymptotically locally Euclidean (ALE) case. At the end of the talk, I will discuss how this stability analysis could potentially be used to extend the Ricci flow beyond singularities of certain kind.