# Mathematical Sciences Research Institute

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# Seminar

Geometric Analysis: Convergence of Ricci flows with bounded scalar curvature March 10, 2016 (11:00 AM PST - 12:00 PM PST)
Parent Program: Differential Geometry MSRI: Simons Auditorium
Speaker(s) Richard Bamler (University of California, Berkeley)
Description No Description
Video
Abstract/Media

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.