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Topology/Geometry Seminar

On the spectral geometry of manifolds with conic singularities

Asilya Suleymanova, Max Planck Institute, Germany

Location:  Hill 525
Date & time: Tuesday, 31 October 2017 at 3:30PM - 4:30PM

Abstract:  In this talk we consider the heat kernel of the Laplace-Beltrami operator on a Riemannian manifold. On any closed smooth Riemannian manifold the heat trace expansion gives some geometrical information such as dimension, volume and total scalar curvature of the manifold. On a manifold with conic singularities we derive a detailed asymptotic expansion of the heat trace using the Singular Asymptotics Lemma of Jochen BrĂ¼ning and Robert T. Seeley. Then we investigate how the terms in the expansion reflect the geometry of the manifold. Can one hear a singularity?

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Department of Mathematics

Department of Mathematics
Rutgers University
Hill Center - Busch Campus
110 Frelinghuysen Road
Piscataway, NJ 08854-8019, USA

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