Spectral Gap for Random Schottky Surfaces

Explore a mathematical seminar presentation examining the spectrum of the Laplacian on Riemannian manifolds, with particular focus on hyperbolic surfaces. Delve into groundbreaking research conducted by Irving Calderón in collaboration with M. Magee and F. Naud, investigating spectral gap properties for random Schottky surfaces - hyperbolic surfaces of infinite area without cusps. Learn how this research intersects with Geometry, Dynamics, Number Theory, and Probability, while understanding its connection to Selberg's 1/4-Conjecture. Discover the fascinating implications of this work for understanding the behavior of Laplace eigenvalues on typical hyperbolic surfaces, contributing to a rich mathematical theory that continues to reveal new insights in the field of Spectral Geometry.