Spectral Analysis: Hyperbolic Surfaces

This lecture covers the spectral analysis of hyperbolic surfaces, focusing on the trace formula and its applications in understanding the geometric and spectral properties of these surfaces. The instructor discusses the trace formula in the context of GL₂(R) and SL₂(R), highlighting the importance of cocompactness and unitary representations. Various concepts such as Selberg kernels, trace-class operators, and integral operators are explored, providing insights into the spectral theory of hyperbolic surfaces.