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Thursday, November 1, 2018

**Abstract:** If M is a compact manifold of negative curvature, Laplace eigenfunctions on M with large eigenvalue are expected to behave chaotically, reflecting the correspondence principle between classical and quantum mechanics. I will describe this chaotic behavior, and explain what can be proved about it using methods from harmonic analysis. I will also explain why harmonic analysis alone has a hard time giving us the complete picture, and how we can see more of it using tools from number theory.