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Type-II singularities of Ricci flow

PDE and Applied Math Seminar

Speaker: Dan Knopf , University of Texas Austin
Location: 1147 MSB
Start time: Tue, Nov 12 2013, 2:10PM

Ricci flow is a powerful tool for probing the geometry and topology of Riemannian manifolds. From the analytic point of view, it is a quasilinear weakly parabolic diffusion-reaction system for an evolving Riemannian metric. Because of the reaction terms present, finite-time singularity formation is inevitable for large classes of initial data. It is therefore natural to want to know as much as possible about what singular behaviors are possible. We will review some of what is known about the classification of singularity types, and we will discuss recent progress (by the speaker and collaborators) in determining the rates at which singularities can form.