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Friday, February 15, 2019

**Abstract:** The Laplacian operator acting on functions on a Riemannian manifold is an analytic operator invariant under isometry of the manifold. Its spectrum encodes much geometric information of the manifold. In this talk, I will start with some basic properties of Laplacian operator and hyperbolic geometry. Then I will talk about how these two interact with each other. Time permitting, I will talk about some of my recent works. No background on Laplacian operator or hyperbolic geometry is assumed.