Explore the intricacies of Goe and Gue statistics for Random Covers of Hyperbolic Surfaces in this hour-long seminar presented by Frédéric Naud at the Centre de recherches mathématiques (CRM). Delve into topics such as the Goe curve, semiclassical problems, and recent results in the field. Examine the concepts of covers, twisted Laplacians, and limits, before moving on to generalizations and key ingredients. Gain insights into trace formulas, FN of gamma, and Chi-square distributions as they relate to hyperbolic surfaces. This talk, part of the Spectral Geometry in the clouds seminar series, offers a comprehensive look at advanced mathematical concepts in spectral geometry.