This semester I am teaching Math 8821: Number theory 1. This semester we will cover an Introduction to -adic groups and their representation theory. The class meets at 10:00 AM in Campion Hall 235 on MWF.

Here is the syllabus

We will begin by covering the following topics:

• the basic properties and structure of p-adic fields,
• locally compact, totally disconnected groups and their representation theory
• basic structure theory of reductive groups
• supercuspidal representations and ideas related to the Bernstein decomposition
• later in the semester, special attention will be given to the Iwahori-Hecke algebra and its role.  

The main references will be initially be

–Course notes by Fiona Murnaghan at Toronto

– the Ottawa lectures on Admissible representations of Reductive p-adic groups,

– Iwahori-Matsumoto’s article 

with more references given as we progress.

Problem Sets

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

• Week 1 exercises
• Week 3 exercises
• Week 4 exercises
• Week 5 exercises
• Week 6 exercises
• Weeks 7-8 exercises
• Week 9 exercises