NCMW - Representations of p-adic groups (2022)

Venue: IIT Bombay, Offline Mode

Dates: 23 May 2022 to 4 Jun 2022

 The theory of admissible complex representations of p-adic groups is an important constituent of the Langlands program, and in particular informs research on various areas of number theory such as modular forms, arithmetic geometry etc., in addition to being a topic of intensive research in its own right.
We plan to have a basic (mini-)course on each of the following six topics that come under or is intimately tied to this broad area:

1. Deligne-Lusztig theory of representations of finite groups of Lie type.
2. Representation theory of general linear groups over p-adic fields.
3. Bruhat-Tits theory.
4. Types and construction of supercuspidal representations of p-adic groups (this will use Bruhat-Tits theory).
5. Affine Deligne-Lusztig constructions, the representations of p-adic groups realized in the cohomology of affinne Deligne-Lusztig varieties. This is an evolving area in which much recent progress has been made by Charlotte Chan and her collaborators.
6. Automorphic representations and L-functions (in which lies the origin of the p-adic theory, and which still gives rise to objects in it).

Three of the courses (Deligne-Lusztig theory, Bruhat-Tits theory and the construction of supercuspidal representations) will also serve as background material to let students follow the lectures on the fifth course mentioned above, namely the Affine Deligne-Lusztig constructions. We expect the lectures to be useful to mathematicians working across the country on a diverse set of topics related to the Langlands program, and especially so to the several graduate students, post doctoral researchers and young faculty whose main research interest is the theory of complex representations of p-adic groups.