Differential Geometry Seminar: Ricci Flow of Doubly-warped Product Metrics

Seminar | October 7 | 3-4 p.m. | 939 Evans Hall

 Maxwell Stolarski, Arizona State

 Department of Mathematics

The Ricci flow of rotationally symmetric metrics has been a source of interesting dynamics for the flow that include the formation of slow blow-up degenerate neckpinch singularities and the forward continuation of the flow through neckpinch singularities. A natural next source of examples is then the Ricci flow of doubly-warped product metrics. This structure allows for a potentially larger collection of singularity models compared to the rotationally symmetric case. Indeed, formal matched asymptotic expansions suggest a non-generic set of initial metrics on a closed manifold form finite-time, type II singularities modeled on a Ricci-flat cone at parabolic scales. I will outline the formal matched asymptotics of this singularity formation and the topological argument used to prove existence of Ricci flow solutions with these asymptotics. Finally, we will discuss applications of these solutions to questions regarding the possible rates of singularity formation and the blow-up of scalar curvature.