HEU Number Theory Workshop 2024

Time: Feb. 22nd -- Feb. 23rd
Venume: Room 1101, Building 21B, HEU
Chair: Jun Wang 老王头

The organiser and principal contact is Chao Qin.

The workshop is open to everyone and no registration is necessary.

Title and Abstract

9:00--10:00

Speaker: Meng-Fai Lim
Title: On the fine Tate-Shafarevich group
Abstract: The fine Tate-Shafarevich group of an elliptic curve was first defined by Wuthrich. In this talk we begin presenting certain results on its growth in Zp-extension. From there, we discuss certain topics arising from this study.

10:00--11:00

Speaker: Dong Yan
Title: Remarks on Iwasawa's linearity conjecture for cyclotomic fields
Abstract: We give a sufficient condition such that the λ-invariant of Kubota-Leopoldt p-adic L-function is equal to one for irregular primes. Our proof involves studying the structure of certain cohomology groups of Hida family.

11:00--12:00

Speaker: Luochen Zhao
Title: Explicit differentiation of totally real p-adic Hecke L-functions
Abstract: The leading term of the p-adic Hecke L-function of a totally real field is of arithmetic interest by the Gross--Stark conjecture. When the field is Q, this is witnessed by the combination of the Ferrero--Greenberg formula that relates derivatives to Morita Gamma values and the Gross--Koblitz formula that relates Gamma values to Gauss sums. In this talk I'll report my generalization of the Ferrero--Greenberg formula to the totally real case using the infinite sum expression of p-adic L-functions after Delbourgo.

12:00--14:00

午餐，国际交流中心

14:00--14:30

参观军工纪念馆

14:30--15:30

Speaker: Yangyu Fan
Title: Ichino periods for CM forms
Abstract: Suggested by the conjecture of Sakellaridis-Venkatesh, there shoulb be explicit relations between Ichino periods and Waldspurger toric periods for CM forms. In this talk, we will explain how to establish such relations by theta liftings and the see-saw principle. This is based on a joint work with L. Cai and Y. Jiang.

15:30--16:30

Speaker: Shenxing Zhang
Title: 抓石子游戏中的数学问题
Abstract: 抓石子游戏即Nim游戏是著名的博弈论问题。我们将回顾一维一堆Nim游戏的一些已知结果，给出一些新的结果，并由此提出一个关于其允许的操作集合元素个数增加时，其GS数列性质的一个猜想。最后利用该猜想寻找最终二分的GS数列。

Feb 23rd

自由讨论