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Friday, October 5, 2018

**Abstract:** Concluding our series, we’ll generalize the asymptotics of the first talk to prove a “local” Weyl’s law. Then, we'll use this to prove an Ergodic theorem in the spirit of the Classical-Quantum Correspondence: the "quantum average" of an operator is equal to the "phase space average" of its principal symbol, "almost always". I’ll explain how this can be turned into mathematical statement, how to improve on it, and explain why both number theorists and geometers might care.