From radial symmetry to fractal behavior of aggregation equilibria for repulsive-attractive potentials

Ruiwen Shu (University of Oxford)

01-Oct-2021, 19:00-20:00 (2 years ago)

Abstract: For the interaction energy with repulsive-attractive potentials, we give generic conditions which guarantee the radial symmetry of the local minimizers in the infinite Wasserstein distance. As a consequence, we obtain the uniqueness of local minimizers in this topology for a class of interaction potentials. We introduce a novel notion of concavity of the interaction potential allowing us to show certain fractal-like behavior of the local minimizers. We provide a family of interaction potentials such that the support of the associated local minimizers has no isolated points and any superlevel set has no interior points.

mathematical physicsanalysis of PDEsclassical analysis and ODEscategory theorycomplex variablesfunctional analysislogicmetric geometryoptimization and control

Audience: researchers in the topic


VCU ALPS (Analysis, Logic, and Physics Seminar)

Series comments: Description: Research seminar on topics ranging from analysis and logic to mathematical physics.

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Meeting ID: 951 0562 0974

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Organizer: Ihsan Topaloglu*
Curators: Marco Aldi*, Brent Cody, Sean D. Cox, Alex Misiats, Allison Moore*
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