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Geometry and Topology Seminar

Friday, October 25, 2019
3:00pm to 5:00pm
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Linde Hall 187
Ricci Flow of Doubly-warped Product Metrics
Maxwell Stolarski, School of Mathematical and Statistical Sciences, Arizona State University,

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 discuss the applications of such solutions to questions regarding the possible rates of singularity formation and the blow-up of scalar curvature. In the second half, we will examine in detail the topological argument used to prove the existence of Ricci flow solutions with these dynamics.

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