Efficiently Chopping a Hyperbolic Surface in Two - Cheeger Constants and Spectral Geometry

Explore the concept of efficiently dividing hyperbolic surfaces in this seminar talk from the Spectral Geometry in the clouds series. Delve into the Cheeger constant of Riemannian manifolds and its relationship to the spectral gap of the Laplacian. Examine recent research on the upper bounds of Cheeger constants for hyperbolic surfaces of large genus, demonstrating a uniform gap between these surfaces and the hyperbolic plane. Follow the speaker's journey through the proof, including discussions on Poisson point processes, pointless tessellations, and random subsets. Gain insights into the mathematical intricacies of hyperbolic geometry and spectral analysis in this hour-long presentation by Bram Petri from Sorbonne Université.