1/16, Title: “Representations for GL(2) over local fields and L-functions”
Speaker: Fu-Tsu Wei (NCU)
Classification of irreducible admissible representations of GL(2) over local fields of char. zero, Whittaker models, Kirillov models, The definitions of local zeta integrals and local L-functions for GL(1) and GL(2), functional equations.

1/17, Title: "Representations for GL(2) over number fields and L-functions”
Speaker: Ming-Lun Hsieh (AS)
Hecke algebras and tensor product theorem, Global zeta integrals for automorphic forms, global L-functions and functional equation and converse theorem

1/18, Title: “The Shimura-Waldspurger theta correspondence”
Speaker: Shih-Yu Chen (NTU)
Weil representations over local and global fields for O(m)xSp(n), explicit Shimura-Waldspurger correspondence, Waldspurger formula

1/19, Title: “Trace formula and Jacquet-Langlands correspondence”
Speaker: Yao Cheng (NTU)
Introduce necessary tools in trace formula to explain a proof of Jacquet-Langlands correspondence.

Reference:

(1)  Automorphic representations and L-functions for the general linear group Volume I, Goldfeld and Hundley, Cambridge studies in advanced mathematics 129

(2)  Automorphic forms on GL(2), Lecture notes in mathematics 114

Prerequisites: Basic Algebra and number theory. For example,

The audience is assumed to be familiar with “A course in arithmetic”, Serre, GTM07.