05-12【Maxwell Stolarski 】腾讯会议 Geometry&Topology Seminar系列讲座之016


  Closed Ricci Flows with Singularities Modeled on Asymptotically Conical Shrinkers

报告人:Maxwell Stolarski ( Arizona State University)

时 间:2022年5月120900 -1000  

地 点:腾讯会议ID: 914-3694-1759,密码: 202202


摘 要: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 recent 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.