Group Actions, Homogeneous Dynamics, and Number Theory
群作用、齐次动力学和数论
基本信息
- 批准号:1700109
- 负责人:
- 金额:$ 14.4万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2017
- 资助国家:美国
- 起止时间:2017-06-15 至 2023-05-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Many questions in mathematics come with a set of symmetries that has a so-called group structure. Exploring the dynamics of underlying group actions, namely to study how points in spaces behave under symmetries, has recently played a central role in proving important results and resolving longstanding questions in mathematics. The overall aim of this research project is to advance the technique of using dynamics of group actions as a powerful tool to study questions that arise in algebra, geometry, and number theory, and to gain a deeper understanding of the connections between these mathematical fields.In this project special attention will be given to the following three directions: (1) Develop reduction theory of indefinite integral quadratic forms and consider its generalization to number fields using methods of dynamical systems. (2) Investigate random walks on Lie groups and equidistribution problems in homogenous spaces in light of recent developments in spectral theory and the theory of automorphic forms. (3) Study the height bounds of generators of arithmetic groups incorporating dynamical methods into classical algebraic and geometric theory of arithmetic groups. The project also aims to seek new interactions and develop the techniques in the study of groups, dynamics, and number theory.
数学中的许多问题都伴随着一组具有所谓群结构的对称性。探索潜在群体行为的动力学,即研究空间中的点在对称性下如何表现,最近在证明重要结果和解决数学中长期存在的问题方面发挥了核心作用。该研究项目的总体目标是推进使用群行为动力学作为研究代数、几何和数论中出现的问题的有力工具的技术,并更深入地理解这些数学领域之间的联系。在该项目中,将特别关注以下三个方向:(1)发展不定积分二次形式的约简理论,并考虑使用动力系统方法将其推广到数域。 (2)根据谱理论和自守形式理论的最新发展,研究李群上的随机游走和齐次空间中的均匀分布问题。 (3)将动力学方法融入算术群的经典代数和几何理论中,研究算术群生成元的高度界。该项目还旨在寻求新的相互作用并开发群、动力学和数论研究的技术。
项目成果
期刊论文数量(4)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Explicit result on equivalence of rational quadratic forms avoiding primes
有理二次型避免素数等价的显式结果
- DOI:10.1016/j.jnt.2021.02.006
- 发表时间:2021
- 期刊:
- 影响因子:0.7
- 作者:Chan, Wai Kiu;Gao, Haochen;Li, Han
- 通讯作者:Li, Han
On realization of isometries for higher rank quadratic lattices over number fields
数域上高阶二次格的等距实现
- DOI:10.1090/tran/8670
- 发表时间:2022
- 期刊:
- 影响因子:1.3
- 作者:Chan, Wai Kiu;Li, Han
- 通讯作者:Li, Han
On effective equidistribution for quotients of SL(d,ℝ)
关于 SL(d,α) 商的有效均分布
- DOI:10.1007/s11856-020-1978-z
- 发表时间:2020
- 期刊:
- 影响因子:1
- 作者:Aka, M.;Einsiedler, M.;Li, H.;Mohammadi, A.
- 通讯作者:Mohammadi, A.
New bounds in reduction theory of indefinite ternary integral quadratic forms
不定三元积分二次型归约理论的新界限
- DOI:
- 发表时间:2018
- 期刊:
- 影响因子:1.7
- 作者:Li, Han;Margulis, Gregory A
- 通讯作者:Margulis, Gregory A
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Han Li其他文献
Experimental demonstration of fronthaul flexibility for enhanced CoMP service in 5G radio and optical access networks
5G 无线电和光接入网络中增强型 CoMP 服务的前传灵活性实验演示
- DOI:
10.1364/oe.25.021247 - 发表时间:
2017 - 期刊:
- 影响因子:3.8
- 作者:
Jiawei Zhang;Yuefeng Yi;Hao Yu;Xingang Huang;Han Li - 通讯作者:
Han Li
Transparency of graphene membranes to eV-scale electrons
石墨烯膜对电子级电子的透明度
- DOI:
- 发表时间:
2022 - 期刊:
- 影响因子:0
- 作者:
Jiahe Kang;Y. Duan;Wei Gao;Han Li;Changyu Li;Xiao Zhao;Wenlong Li;Chengguang Zhu - 通讯作者:
Chengguang Zhu
Contributions of National Key Forestry Ecology Projects to the forest vegetation carbon storage in China
国家林业生态重点工程对我国森林植被碳储量的贡献
- DOI:
10.1016/j.foreco.2020.117981 - 发表时间:
2020-04 - 期刊:
- 影响因子:3.7
- 作者:
Yu Zhang;Ji Yuan;Chengming You;Rui Cao;Bo Tan;Han Li;Wanqin Yang - 通讯作者:
Wanqin Yang
Comprehensive Study of the Chemical, Physical, and Structural Evolution of Molecular Layer Deposited Alucone Films during Thermal Processing
分子层沉积 Alucone 薄膜在热处理过程中化学、物理和结构演变的综合研究
- DOI:
- 发表时间:
2023 - 期刊:
- 影响因子:8.6
- 作者:
Vamseedhara Vemuri;S. King;W. Lanford;J. Gaskins;P. Hopkins;Jeremy Van Derslice;Han Li;N. Strandwitz - 通讯作者:
N. Strandwitz
Levistolide A Attenuates Alzheimer’s Pathology Through Activation of the PPARγ Pathway
Levistolide A 通过激活 PPARγ 途径减轻阿尔茨海默病的病理学
- DOI:
10.1007/s13311-020-00943-1 - 发表时间:
2020-10 - 期刊:
- 影响因子:5.7
- 作者:
Qu Xiao-Dan;Guan Pei-Pei;Han Li;Wang Zhan-You;Huang Xue-Shi - 通讯作者:
Huang Xue-Shi
Han Li的其他文献
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{{ truncateString('Han Li', 18)}}的其他基金
Collaborative Research: Enabling Scalable Redox Reactions in Biomanufacturing
合作研究:在生物制造中实现可扩展的氧化还原反应
- 批准号:
2328145 - 财政年份:2023
- 资助金额:
$ 14.4万 - 项目类别:
Standard Grant
A Dynamical Systems Weekend Conference at Wesleyan
卫斯理学院动力系统周末会议
- 批准号:
2000176 - 财政年份:2020
- 资助金额:
$ 14.4万 - 项目类别:
Standard Grant
CAREER: Engineering redox metabolism using unnatural cofactors
职业:使用非天然辅助因子工程氧化还原代谢
- 批准号:
1847705 - 财政年份:2019
- 资助金额:
$ 14.4万 - 项目类别:
Standard Grant
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