In this series of expository lectures, I will provide an introductory overview of recent advancements in the spectral analysis of locally symmetric spaces, going beyond the traditional Riemannian framework. This topic is built upon the theory of proper action on reductive homogeneous spaces, which will be presented by F. Kassel in the same week, alongside the theory of global analysis on symmetric spaces and a rapidly developing theory of branching in infinite-dimensional representations of reductive groups. My aim is to clarify key concepts in a non-technical manner, using several elementary examples to make the fundamental ideas more accessible.
© Toshiyuki Kobayashi