Fractal Uncertainty Principle and Spectral Gaps

This lecture by the instructor covers the concepts of Schottky groups, spectral gaps, and the Fractal Uncertainty Principle (FUP). The lecture delves into the Selberg zeta function, v-porous sets, and the relationship between FUP and spectral gaps. It also explores Möbius maps, the limit set of Schottky groups, and their connection to hyperbolic surfaces. Additionally, the lecture discusses transfer operators, the Patterson-Sullivan measure, and their role in analyzing the limit set. Through examples and visuals, the lecture provides a comprehensive understanding of these complex mathematical concepts.