Orateur
Description
This talk is an introduction to the representation theory of p-adic groups aimed at all participants of the trimester program. I will survey the current state of the art and include new developments of the last six months. We will focus on two crucial aspects:
First, I will provide an overview of the construction of all so called supercuspidal representations, which are the building blocks for all representations. For more than 20 years it remained open to extend Yu's general construction to the case p=2, and I will sketch what makes this case so special and how we could overcome the obstacles in my recent joint work with David Schwein.
Second, we will study the structure of the whole category of representations of p-adic groups in terms of these supercuspidal
representations, and I will explain how two recent preprints with Jeffrey Adler, Manish Mishra and Kazuma Ohara allow us to reduce a lot of problems about the (category of) representations of p-adic groups to problems about representations of finite groups of Lie type, where answers are often already known or are at least easier to achieve.
