Closed Ricci Flows with Singularities Modeled on Asymptotically Conical Shrinkers

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• Maxwell Stolarski (University of Warwick)
• Monday 23 January 2023, 14:00-15:00
• CMS, MR13.

If you have a question about this talk, please contact Zexing Li.

Shrinking Ricci solitons are Ricci flow solutions that self-similarly shrink under the flow. Their significance comes from the fact that finite-time Ricci flow singularities are typically modeled on gradient shrinking Ricci solitons. Here, we shall address a certain converse question, namely, “Given a complete, noncompact gradient shrinking Ricci soliton, does there exist a Ricci flow on a closed manifold that forms a finite-time singularity modeled on the given soliton?” We’ll discuss work that shows the answer is yes when the soliton is asymptotically conical. No symmetry or Kahler assumption is required, and so the proof involves an analysis of the Ricci flow as a nonlinear degenerate parabolic PDE system in its full complexity. We’ll also discuss applications to the (non-)uniqueness of weak Ricci flows through singularities.

This talk is part of the Partial Differential Equations seminar series.

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