Séminaires : Séminaire d'Analyse et Géométrie

Equipe(s) :
Responsables :O. Biquard, A. Deruelle, E. Di Nezza, I. Itenberg, X. Ma
Email des responsables : {olivier.biquard, alix.deruelle, eleonora.dinezza, ilia.itenberg, xiaonan.ma}@imj-prg.fr
Salle : 15–25.502
Adresse :Jussieu

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Orateur(s) Maxwell Stolarski - Warwick University,
Titre Closed Ricci Flows with Singularities Modeled on Asymptotically Conical Shrinkers
Horaire14:00 à 15:00
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.