I will be on leave during Fall 2026.

In Fall 2025-Spring 2026, I taught a two semester course on representation theory of p-adic reductive groups. Below is the summary of the second course. I am leaving this here as an embarrassing reminder to upload my notes and problem sets for both semesters.

Math8822: Number theory 2

This semester we will continue our Introduction to -adic groups and their representation theory. The class meets at 1:00pm on MWF in Maloney 560.

Here is the syllabus

This class will focus on the “spherical aspects” of the theory. Topics will include:

• affine root systems and Weyl groups in the context of p-adic groups,
• the Iwahori and spherical Hecke algebras, 
• equivalence between Iwahori-spherical reps and affine Hecke-modules.
• the Langlands dual group and the Satake isomorphism
• Whittaker models and the Casselman–Shalika formula 

After covering these topics, we will turn to some variants arising in the “relative Langlands program,” covering some basic structure theory of spherical varieties and the relative Satake isomorphism relating the unramified Plancherel density of nice spherical varieties to special values of L-functions.

Aside from text’s like Bump’s “Automorphic forms and representations” and Getz–Hahn, our main references will

• This article on Iwahori-Hecke algebras
• Iwahori-Matsumoto’s article 
• Sakellaridis’ work on Spherical functions on spherical varieties

I will add more as things progress

Problem Sets

These will be (for the most part) the exercises which I assign during lecture.