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This seminar talk from the "Spectral Geometry in the clouds" series explores the spectral statistics of negatively curved surface covers. Presented by Julien Moy from Orsay on February 17, 2025, the lecture addresses the Bohigas-Giannoni-Schmit (BGS) conjecture from the early 1980s regarding spectral distribution in quantum systems with chaotic classical limits. Learn about how this conjecture proposes that such systems should display spectral statistics predicted by Random Matrix Theory (RMT) in the high energy limit. Discover recent developments focused on random models of quantum systems and examine specific results on the spectral distribution of the Laplacian on random covers of surfaces with variable negative curvature. The presentation demonstrates how, in the limit of large degree, the smoothed counting function of eigenvalues exhibits fluctuations that align with Random Matrix Theory predictions.
