Geometric Analysis and Topology Seminar

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Convergence of Ricci Flows with Bounded Scalar Curvature

Speaker: Richard Bamler, UC Berkeley

Location: Warren Weaver Hall 517

Date: Friday, February 26, 2016, 11 a.m.

Synopsis:

It is a basic fact that the Riemannian curvature becomes unbounded at every finite-time singularity of the Ricci flow. Sesum showed that the same is true for the Ricci curvature. It has since remained a conjecture whether also the scalar curvature becomes unbounded at any singular time. In this talk I will show that, given a uniform scalar curvature bound, the Ricci flow can only degenerate on a set of codimension bigger or equal to 4, if at all. This result is a consequence of a structure theory for such Ricci flows, which relies on and generalizes recent work of Cheeger and Naber.