Spectrum of Hyperbolic Surfaces

This lecture explores the spectrum of hyperbolic surfaces, focusing on Fuchsian groups and their actions. The instructor discusses fixed points, hyperbolic and parabolic elements, lattice structures, and continuous actions on surfaces. The lecture also covers the classification of Fuchsian groups and their connection to rotations along spheres. Various observations and definitions related to hyperbolic surfaces are presented, along with the concept of lattices. The lecture delves into the properties of hyperbolic and parabolic elements, emphasizing their significance in the context of Fuchsian groups.