Explore new upper bounds on geometric and spectral invariants of closed hyperbolic surfaces in this 57-minute seminar talk from the Spectral Geometry in the clouds series. Delve into joint work by Maxime Fortier Bourque and Bram Petri, focusing on both low and high genus surfaces. Learn about their innovative approach using the Selberg trace formula and test functions, inspired by Cohn and Elkies' work on Euclidean sphere packing density. Gain insights into advanced mathematical concepts and techniques applied to hyperbolic geometry and spectral theory.