**
Maxwell Stolarski, Arizona State University**

**Title:** Closed Ricci Flows with Singularities Modeled on
Asymptotically Conical Shrinkers

**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 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.