Modular forms from the algebraic geometric point of view
Student No.:40
Time:Mon & Thu, 8:00-9:35
Instructor:Chen Zongbin  
Place:Conference Room 3, Jin Chun Yuan West Bldg.
Starting Date:2018-3-5
Ending Date:2018-6-14

This course has several objectives, depending on the progress. The first objective is to explain Deligne’s proof of Ramanujan’s conjecture for the \tau-function, for which we need to study the geometry of modular curves. The second objective is to explain Langlands’ approach to counting points on the modular curves over finite fields. If we have time, we will go on to explain Deligne and his followers’ proof of the local Langlands correspondence for GL_2.

Prerequisite: Algebraic geometry, Group representations

Deligne, Formes modulaires et représentations l-adiques.
Deligne, Letter to Piatetski-Shapiro.
Langlands, Modular forms and l-adic representations.