Learning seminar: Trace Formulae
This is the website for the learning seminar about the trace formula organized by Héctor del Castillo and Andrei Seymour-Howell. In this seminar, we will cover the basics of the trace formula, aiming towards explicit trace formulae results in the co-compact case and explore ideas for extending the trace formula beyond this case.
The seminar will take place in Room 205 of the Education Convergence Building at Chonnam National University, Gwangju. The weekly schedule is Tuesday at 11:00 am. The seminar will be based on the following references:
| Date | Speaker | Subject | Extra |
|---|---|---|---|
| 18/11/2025 | Héctor del Castillo |
Induced representation and distributions. Topics around Sections 1 and 2 of D. Whitehouse. |
Notes |
| 25/11/2025 | Héctor del Castillo |
Kernels and Traces. Topics around Sections 1 and 2 of D. Whitehouse. |
Notes |
| 02/12/2025 | Héctor del Castillo |
Trace formula and application. Topics around Sections 1 and 2 of D. Whitehouse. |
|
| Date | TBA |
We introduce the concept of Hilbert-Schmidt and trace-class operators. Section 3.1 of D. Whitehouse and Section 9.1, 16.1 and 16.2 of Getz and Hahn. |
|
| Date | TBA |
We review basic on adèles and algebraic groups to define. |
|
| Date | TBA |
We survey around the cuspidal spectrum. The main result to cover is that the cuspidal subspace the regular representation is trace class. Chapter 9 of Getz and Hahn. |
|
| Date | TBA |
Section 18.2 of Getz and Hahn. |
|
| Date | TBA |
Co-compact case and reduction to SL(2). Survey around Section 5.6 of Chapter 1 of I. M. Gelfand, M. I. Graev, I. I. Pyatetskii-Shapiro. |
|
| Date | TBA |
Survey around Section of 18.7 Getz and Hahn. |
|
| Date | TBA |
Survey around Section 4 of D. Whitehouse. |
|
| Date | TBA |
Survey around Section 6-7 of D. Whitehouse. |
