Course MAT518

Topics in Automorphic Forms: Philosophy of cusp forms

In this course, we will focus on some aspects of the foundation of automorphic forms.  A general organization principle is that cusp forms should be the fundamental building blocks of the theory, which has many implications both to arithmetic and to local representation theory.  The first part of the course will be a rigorous introduction to this circle of ideas.  The aim is to give precise definitions in arbitrary dimension.  The second part will be concerned with the structure of representations of real Lie groups, notably the Langlands classification, cohomological representations, the tempered dual and Vogan theory.