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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.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].