Title: Ricci solitons, conical singularities, and nonuniqueness
Abstract: In dimension n=3, there is a complete theory of weak
solutions of Ricci flow -- the singular Ricci flows introduced by
Kleiner and Lott. These are unique across singularities, as was proved
by Bamler and Kleiner. In joint work with Angenent, we show that
uniqueness should not be expected to hold for Ricci flow weak
solutions in dimensions n>4, not even topologically. Specifically, we
exhibit a discrete family of asymptotically conical gradient shrinking
soliton singularity models, each of which admits non-unique forward
continuations by gradient expanding solitons.