Seminar Number Theory
Student No.:40
Time:Mon 15:20-16:55, Oct.08-Jan.14
Instructor:Fu Lei, Xu Bin, Cai Li, Chen Zongbin, Chun-Yin Hui, Wang Haoran, Li Yongxiong, Liu Yu  
Place:Lecture Hall, Jin Chun Yuan West Bldg.
Starting Date:2018-10-8
Ending Date:2019-1-14


Speaker: Xu Shen (Morningside center, CAS)

Title: p-adic period domains and the Fargues-Rapoport conjecture

In his 1970 ICM report, Grothendieck asked the question to describe the p-adic analogues of Griffiths period domains. In this talk, we will review some constructions for these p-adic period domains, following recent developments in p-adic Hodge theory. We will then explain some ideas in a proof of the Fargues-Rapoport conjecture about the structure of certain p-adic period domains. This is joint work with Miaofen Chen and Laurent Fargues.


Speaker: Xin Wan (Morningside center, CAS)

Title: Iwasawa theory and BSD formula for GL(2)

We first give an overview of recent results on Iwasawa theory and applications to BSD formulas for elliptic modular forms. Then we explain some ingredients used for the argument.


Speaker: Xinyi Yuan [U. C. Berkeley & IAS Tsinghua]

Title: Modular heights of Shimura curves

In this talk, I will introduce a formula expressing the modular height of a quaternionic Shimura curve over a totally real field in terms of the logarithmic derivative at 2 of the Dedekind zeta function of the totally real field. The proof of the formula is inspired by the previous work of Yuan-Zhang-Zhang on the Gross-Zagier formula.