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 Brüning and Robert T. Seeley. Then we investigate how the terms in the expansion reflect the geometry of the manifold. Can one hear a singularity?