Organizer: Shaoyun Yi

Email: yishaoyun926@xmu.edu.cn

Office: B515

Tentative Schedule:

Week No.	Date	Topics	Speaker	No. of Students
1	9/11	Jordan induction of Arthur packet and a support equality (Abstract)	Jiawei Yang (杨嘉维)	10
2	9/18	Dirichlet's Theorem and the Development of Modern Number Theory (1) (Abstract)	Boyi Zheng (郑博弈)	7
3	9/25	No Talk
4	10/2	No Talk
5	10/9	Dirichlet's Theorem and the Development of Modern Number Theory (2) (Abstract)	Boyi Zheng (郑博弈)
6
7
8
9
10
11
12
13
14
15
16

Abstracts

Jiawei Yang - Jordan induction of Arthur packet and a support equality

In this talk, I will discuss Arthur packets for real reductive groups within the microlocal framework of Adams–Barbasch–Vogan. We first introduce the geometric parameter space, equivariant perverse sheaves, and the microlocal characterization of packet membership. We then present recent work by Adams–Ionov–Mason-Brown–Vogan on Jordan induction and the unitarity of microlocal Arthur packets. Finally, we describe a support equality theorem, which identifies these packets with the irreducible constituents obtained from suitable unipotent packets via cohomological induction followed by real normalized parabolic induction. We emphasize the interplay between coherent continuation, geometric convolution, and microlocal support, explaining how these tools control individual constituents beyond the information given by virtual character identities. This support equality is established in my recent work.

Boyi Zheng - Dirichlet's Theorem and the Development of Modern Number Theory (1)

This lecture explains Dirichlet's most classical proof using the class number formula. It begins with the prime number theorem and Dirichlet characters, and proceeds to the nonvanishing property of Dirichlet $L$-functions for non-real characters. The real-character case is postponed to the next lecture due to the length of the class number formula.

Boyi Zheng - Dirichlet's Theorem and the Development of Modern Number Theory (2)

TBD