Automorphic Kernels: Heat Equation Solutions

This lecture covers the concept of automorphic kernels and their application in solving the heat equation. The instructor discusses the smooth families of solutions and their extensions, emphasizing the unique solutions obtained. Various mathematical notations and properties are explored, such as self-adjointness and positivity. The lecture delves into the continuity of functions and the implications for heat kernel solutions. Key topics include the heat equation, initial conditions, and the uniqueness of solutions. The presentation concludes with a detailed analysis of the properties of automorphic kernels and their role in solving differential equations.