Program
Geometric Representation Seminar
Student No.:40
Time:Fri 15:20-16:20, Oct.12-Jan.18
Instructor:Shan Peng  
Place:Conference Room 3, Jin Chun Yuan West Bldg.
Starting Date:2018-10-12
Ending Date:2019-1-18

2018-10-12

Speaker: 胡永泉 Yongquan Hu (Chinese Academy of Sciences)

Title: Dimensions of Bianchi modular forms and mod p representations of GL2(Qp)

Abstract: Given a level $N$ and a weight $k$, we know the dimension of the space of (classical) modular forms. This turns out to be unknown if we consider Bianchi modular forms, that is, modular forms over imaginary quadratic fields. In this talk, we consider the asymptotic behavior of the dimension when the level is fixed and the weight grows. I will first explain an upper bound obtained by Marshall using Emerton's completed cohomology and the theory of Iwasawa algebras. Then I will review the mod p representation theory of GL2(Qp) and explain how to use it to improve this bound.