Algebraic Cycles and L-functions
代数圈和 L 函数
基本信息
- 批准号:2401337
- 负责人:
- 金额:$ 23万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2024
- 资助国家:美国
- 起止时间:2024-07-01 至 2027-06-30
- 项目状态:未结题
- 来源:
- 关键词:
项目摘要
The research in this project concerns one of the basic questions in mathematics: solving algebraic equations. The information of the solutions are encoded in various mathematical objects: algebraic cycles, automorphic forms and L-functions. The research will deepen the understanding of these mathematical objects and the connection between them, especially in high dimensions, which requires solving many new problems, developing new tools and interactions in diverse areas, and appealing to new perspectives which may shed new light on old problems. It will also advance the techniques for understanding the arithmetic of elliptic curves, particularly the Birch and Swinnerton-Dyer conjecture, one of the seven Millennium Prize Problems of the Clay Mathematics Institute. The PI will continue to mentor graduate students, organize conferences and workshops, and write expository articles. The PI will work on several projects relating arithmetic geometry with automorphic L-function, centered around the common theme of the generalization and applications of the Gross--Zagier formula. The PI will investigate the Kudla--Rapoport conjecture for parahoric levels. The PI will extend the arithmetic inner product formula to orthogonal groups, and study the Bloch--Kato conjecture of symmetric power motives of elliptic curves and endoscopic cases of the arithmetic Gan--Gross--Prasad conjectures. The PI will also investigate a new arithmetic relative trace formula approach towards a Gross--Zagier type formula for orthogonal Shimura varieties.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
本课题的研究涉及数学中的一个基本问题:求解代数方程。解的信息被编码成各种数学对象:代数循环、自同构形式和l函数。这项研究将加深对这些数学对象及其之间的联系的理解,特别是在高维中,这需要解决许多新问题,开发新的工具和在不同领域的相互作用,并吸引新的视角,这可能会对旧问题产生新的启示。它还将推进理解椭圆曲线算法的技术,特别是Birch和Swinnerton-Dyer猜想,它是克莱数学研究所的七个千年奖问题之一。PI将继续指导研究生,组织会议和研讨会,并撰写说明性文章。PI将在几个与自同构l函数相关的算术几何项目上工作,围绕Gross- Zagier公式的推广和应用这一共同主题。PI将研究库德拉-拉波波特猜想的副水平。PI将算术内积公式推广到正交群,并研究椭圆曲线对称幂动机的Bloch—Kato猜想和算术Gan—Gross—Prasad猜想的内镜情况。PI还将研究一种新的算术相对迹公式方法,用于正交Shimura变量的Gross- Zagier型公式。该奖项反映了美国国家科学基金会的法定使命,并通过使用基金会的知识价值和更广泛的影响审查标准进行评估,被认为值得支持。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Chao Li其他文献
The anaerobic and starving treatment eliminates filamentous bulking and recovers biocathode biocatalytic activity with residual organic loading in microbial electrochemical system
厌氧和饥饿处理消除了丝状膨胀并恢复了微生物电化学系统中残余有机负载的生物阴极生物催化活性
- DOI:
10.1016/j.cej.2020.127072 - 发表时间:
2020 - 期刊:
- 影响因子:15.1
- 作者:
Chao Li;Weihua He;DanDan Liang;Yan Tian;Ravi Shankar Yadav;Da Li;Junfeng Liu;Yujie Feng - 通讯作者:
Yujie Feng
Metastasis of renal cell carcinoma to a haemangioblastoma of the medulla oblongata in von Hippel–Lindau syndrome
冯·希佩尔-林道综合征肾细胞癌向延髓血管母细胞瘤的转移
- DOI:
- 发表时间:
2010 - 期刊:
- 影响因子:2
- 作者:
J. Xiong;Shu;Yin Wang;Jing;Chao Li;Y. Mao - 通讯作者:
Y. Mao
A 25-year cross-sequential analysis of self-reported problems: Findings from 5 cohorts from the Spinal Cord Injury Longitudinal Aging Study.
对自我报告问题的 25 年交叉序列分析:脊髓损伤纵向衰老研究 5 个队列的结果。
- DOI:
- 发表时间:
2020 - 期刊:
- 影响因子:4.3
- 作者:
Chao Li;Jillian M. Clark;James S. Krause - 通讯作者:
James S. Krause
An IoT Crossdomain Access Decision-Making Method Based on Federated Learning
一种基于联邦学习的物联网跨域访问决策方法
- DOI:
10.1155/2021/8005769 - 发表时间:
2021-12 - 期刊:
- 影响因子:0
- 作者:
Chao Li;Fan Li;Zhiqiang Hao;Lihua Yin;Zhe Sun;Chonghua Wang - 通讯作者:
Chonghua Wang
Routing Clustering Protocol for 3D Wireless Sensor Networks Based on Fragile Collection Ant Colony Algorithm
基于脆弱集合蚁群算法的3D无线传感器网络路由分簇协议
- DOI:
10.1109/access.2020.2982691 - 发表时间:
2020 - 期刊:
- 影响因子:3.9
- 作者:
Tianyi Zhang;Geng Chen;Qingtian Zeng;Ge Song;Chao Li;Hua Duan - 通讯作者:
Hua Duan
Chao Li的其他文献
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{{ truncateString('Chao Li', 18)}}的其他基金
Scalar curvature and geometric variational problems
标量曲率和几何变分问题
- 批准号:
2303624 - 财政年份:2023
- 资助金额:
$ 23万 - 项目类别:
Standard Grant
Geometric Variational Problems and Scalar Curvature
几何变分问题和标量曲率
- 批准号:
2202343 - 财政年份:2021
- 资助金额:
$ 23万 - 项目类别:
Standard Grant
Arithmetic Geometry and Automorphic L-Functions
算术几何和自同构 L 函数
- 批准号:
2101157 - 财政年份:2021
- 资助金额:
$ 23万 - 项目类别:
Continuing Grant
Geometric Variational Problems and Scalar Curvature
几何变分问题和标量曲率
- 批准号:
2005287 - 财政年份:2020
- 资助金额:
$ 23万 - 项目类别:
Standard Grant
Heegner Points, L-Functions of Elliptic Curves, and Generalizations
海格纳点、椭圆曲线的 L 函数和概括
- 批准号:
1802269 - 财政年份:2018
- 资助金额:
$ 23万 - 项目类别:
Standard Grant
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