会议时间： 2024年6月8日
9：00—17：00
会议地点：华北电力大学(北京市昌平区) 主楼B305
邀请报告人
报告人 工作单位
胡永泉 教授 中国科学院
欧阳毅 教授 中国科学技术大学
田一超 教授 中国科学院
肖梁 教授 北京大学
杨同海 教授 美国威斯康星大学
郑维喆 教授 中国科学院
组织单位：华北电力大学 数理学院
组织者：郭宝珠 杜托平
2024华北电力大学数论学术会议
报告安排 |
主持人 |
上 午 |
9：00-9:50 |
杨同海 |
Arithmetic of Eisenstein Series |
田一超 |
学术自由讨论 |
10：00-10:50 |
欧阳毅 |
Isogeny-based cryptosystems and structure of isogeny graphs |
学术自由讨论 |
11：00-11:50 |
郑维喆 |
平展上同调和超积 |
胡永泉 |
学术自由讨论 |
12：00-14：00 |
午休 |
下午 |
14：00-14:50 |
肖梁 |
Zigzag pattern for reductions of (phi, Gamma)-modules |
胡永泉 |
学术自由讨论 |
15：00-15:50 |
田一超 |
Level raising on unitary Shimura varieties of even rank |
肖 梁 |
学术自由讨论 |
16：00-16:50 |
胡永泉 |
On p-adic Jacquet-Langlands Correspondence for GL(2,Qp) |
学术自由讨论 |
学术报告简介
1、
报告人：杨同海
题目： Arithmetic of Eisenstein Series
摘要：In this talk, I will give an informal and incomplete survey on arithmetic of Eisenstein series related to Siegel-Weil formula, including classical, geometric, and arithmetic Siegel-Weil formula and perhaps their applications if time permits.
2、
报告人：欧阳毅
题目：Isogeny-based cryptosystems and structure of isogeny graphs
摘要：Supersingular elliptic curve Isogeny-based cryptography is one route for post-quantum cryptography. In this talk, we shall explain the mathematical problems on isogeny computation and the cryptosystems based on those problems. We’ll then focus on the study of the isogeny graphs of supersingular elliptic curves and of superspecial abelian surfaces. We will explain several results about the local structure of these graphs. This is based on joint works with Zheng Xu, Songsong Li and Zijian Zhou.
3、
报告人：郑维喆
题目：平展上同调和超积
摘要： 平展上同调的超积提供了代数簇的一族Weil上同调理论，其性质与ℓ进上同调的ℓ无关性和无扭性密切相关。本报告将介绍超积上同调研究的新进展，包括权重理论以及对于分解定理的应用。报告内容基于与Anna Cadoret的合作。
4、
报告人：肖梁
题目：Zigzag pattern for reductions of (phi, Gamma)-modules
摘要: Fontaine established an equivalence between p-adic Galois representations and etale (phi, Gamma)-modules; this has proven to be extremely useful when studying p-adic variations of Galois representations. An interesting question inspired by the study of slopes of modular forms is to compute explicitly the reduction of rank two (etale) triangulline (phi, Gamma)-modules. Numerically, the reduction of these triangulline (phi, Gamma)-modules are locally constant and varies in a "zigzag" way as dictated by so-called Emerton-Gee stack; this was independently observed by Bergdall-Pollack, Rufei Ren, and myself, in different setups. In this talk, I will first explain this zigzag pattern, and give a rather preliminary report on the joint work in progress with John Bergdall, Brandon Levin, and Yong-Suk Moon, in which we study this zigzag pattern over the boundary of the weight space.
5、
报告人：田一超
题目：Level raising on unitary Shimura varieties of even rank
摘要： In this talk, I will explain an analogue of Ribet’s level raising result on the Shimura varieties attached to a unitary group of even rank. The proof is based on a detailed study of the nearby cycle sheaf of some etale local system on the unitary Shimura variety. The whole result is one of the key geometric ingredients on my recent joint work with Yifeng Liu and Liang Xiao on the anti-cyclotomic Iwasawa main conjecture for Rankin--Selberg motives.
6、
报告人：胡永泉
题目: On p-adic Jacquet-Langlands Correspondence for GL(2,Qp)
摘要: The classical Jacquet-Langlands (J-L) correspondence relates complex smooth representations of GL(n) and that of its inner forms. It was proved in 1970's and provides one of the first examples of the functoriality conjecture in Langlands program. However, when we consider representations with p-adic or mod p coefficients, the analogue of J-L correspondence is still poorly understood, even in the simplest case of GL(2,Qp). In this talk, I will report some recent progress on the p-adic and mod p local J-L correspondence for GL(2,Qp). This is joint work with Haoran Wang.
