Room 515, Cosmology Building, National Taiwan University + Cisco WebEx, Physical+Online Seminar

(實體+線上演講 台灣大學次震宇宙館515研討室+ Cisco WebEx)

Closed Ricci Flows with Singularities Modeled on Asymptotically Conical Shrinkers

Maxwell Stolarski (University of Warwick)

**Abstract**

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. These Ricci flows can be shown to exist on a broad class of topologies. In particular, no symmetry or Kahler assumption is assumed, and so the proof involves an analysis of the Ricci flow as a nonlinear degenerate parabolic PDE system in its full complexity.

Meeting number (access code): 2515 905 1865

Meeting password: dqDHx5GKm44

**Organizers:** Nicolau Sarquis Aiex (NTNU), Chung-Jun Tsai (NTU), Siao-Hao Guo (NTU)