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. | 
