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Explore fundamental conjectures in quantum chaos through this mathematical physics colloquium delivered by Jens Marklof from the University of Bristol. Discover recent progress toward understanding how quantum energy level statistics should follow a Poisson point process for completely integrable systems or random matrix theory for chaotic classical dynamics. Examine the specific case of the Laplacian on flat tori, where the problem reduces to analyzing the distribution of quadratic form values at integers, connecting to the classical Oppenheim conjecture. Learn about the Laplacian on compact hyperbolic surfaces and review recent evidence for random matrix statistics emergence in high genus limits. Gain insights into how this interdisciplinary research bridges analysis, geometry, number theory, and mathematical physics, with content designed to be accessible to researchers across multiple mathematical disciplines.
