Tsinghua Icon Number Theory Group at Tsinghua University

Slopes of modular forms

Time: Thu, 6 Jun 2019, 13:30-15:05

Place: First conference room at Jinchunyuan West Building (近春园西楼)

Speaker: Bin Zhao (MCM, AMSS)

Abstract:

In this talk, I will first explain the motivation to study the slopes of modular forms. It has an intimate relation with the geometry of eigencurves. I will mention two conjectures on the geometry of eigencurves: the halo conjecture concerning the boundary behavior, and the ghost conjecture concerning the central behavior. I will then explain some known results towards these conjectures. The former one is a joint work with Rufei Ren, which generalizes a previous work of Ruochuan Liu, Daqing Wan and Liang Xiao. The latter one is a joint work in progress with Ruochuan Liu, Nha Truong and Liang Xiao.