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	9/19	2.1 - 2.3	Adeles, Adelic points of affine schemes, Relationship with restricted direct products
2	9/26	2.4	Hyperspecial subgroups and models I
3	10/10	2.4 - 2.5	Hyperspecial subgroups and models II, Approximation in affine algebraic groups
4	10/17	2.6 - 2.7	The adelic quotient, Reduction theory
5	10/24	3.1 - 3.2	Representations of locally compact groups, Haar measures on locally compact groups
6	10/31	3.3 - 3.6	Gelfand-Pettis integrals, Convolution algebras of test functions,     Haar measures on local fields, Haar measures on the points of affine algebraic groups I
7	11/7	3.6 - 3.11	Haar measures on the points of affine algebraic groups II, Discrete automorphic representations,     The Fell topology, Type I groups, Decomposition of representations, Why affine groups?
8	11/21	4.1 - 4.3	The passage between analysis and algebra, Smooth vectors, Restriction to compact subgroups
9	11/28	4.4 - 4.5	$(\mathfrak{g}, K)$-modules, Hecke algebras with $K$-types
10	12/5	4.6 - 4.9	Infinitesimal characters, Classification of $(\mathfrak{g}, K)$-modules for $\mathrm{GL}_{2\mathbb{R}}$,     Matrix coefficients, The Langlands classification