Organizer: Shaoyun Yi
Speaker: Jiawei Yang (杨嘉维)
Participant: Chuhui Gao (高楚辉)
Reference:
An Introduction to Automorphic Representations - With a view toward trace formulae (GTM 300), Jayce R. Getz and Heekyoung Hahn
Tentative Schedule:
| No. | Date | Sections | Topics |
| 1 | 3/11 | Automorphic Representation Lecture 1 | Abstract |
| 2 | 3/20 (F) | Automorphic Representation Lecture 2 | Abstract |
| 3 | 4/1 | Automorphic Representation Lecture 3 | Abstract |
| 4 | 4/8 | Automorphic Representation Lecture 4 | Abstract |
| 5 | 4/15 | Automorphic Representation Lecture 5 | Abstract |
| 6 | 4/22 | Automorphic Representation Lecture 6 | Abstract |
Abstracts
Automorphic Representation Lecture 1
For the first session of our second seminar on automorphic representation, I will give a rough overview of our seminar, which consists of Langlands' decomposition of the $L^2$-spectrum of the adelic quotient group for the first half, and the (relative) trace formula for the second half. We will start from the cuspidal spectrum of the $L^2$-spectrum.
Automorphic Representation Lecture 2
This time, we will develop the theory of Poincaré series and use this technique to prove the closedness of the cuspidal $L^2$-spectrum in the whole $L^2$-spectrum.
Automorphic Representation Lecture 3
This time, we will take up the discussion on the deduction of the discreteness of the spectrum, and give a sufficient condition for an operator to be of trace class, which is crucial in the (number field case) proof of the second part of Theorem 1.2 discussed in the next section.
Automorphic Representation Lecture 4
This time, we will first finish the proof of the sufficient condition for an operator to be of trace class. After that, we will begin to prove our main theorem for the number field case via this condition using a basic estimate.
Automorphic Representation Lecture 5
We will still work on the basic estimate.
Automorphic Representation Lecture 6
We will finish the estimate in the number field case. After that, we will turn to the function field case, which is much easier than before obviously. Hopefully, we will take about rapidly decreasing functions.