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Toral symmetries of collapsed ancient homogeneous Ricci flows

Recent progress on geometric analysis and Riemannian geometry October 21, 2024 - October 25, 2024

October 24, 2024 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Anusha Mangala Krishnan (Indian Institute of Technology Bombay)
Location: SLMath: Eisenbud Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Toral symmetries of collapsed ancient homogeneous Ricci flows

Abstract

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Collapsed ancient solutions to the homogeneous Ricci flow on compact manifolds occur only on the total space of principal torus bundles. Under an algebraic assumption that guarantees flowing through diagonal metrics and a tameness assumption on the collapsing directions, we prove that such solutions have additional symmetries, i.e., they are invariant under the right action of their collapsing torus. As a byproduct of these additional torus symmetries, we prove that these solutions converge, backward in time, in the Gromov-Hausdorff topology to an Einstein metric on the base of a torus bundle.  (Joint work with F. Pediconi and S. Sbiti.)

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Toral symmetries of collapsed ancient homogeneous Ricci flows

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