The Brumer-Stark Conjecture and its Refinements
布鲁默-斯塔克猜想及其改进
基本信息
- 批准号:2200787
- 负责人:
- 金额:$ 55万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2022
- 资助国家:美国
- 起止时间:2022-07-01 至 2027-06-30
- 项目状态:未结题
- 来源:
- 关键词:
项目摘要
This project concerns algebraic number theory, a branch of mathematics that aims to study properties of the basic number systems arising from roots of polynomials (called number fields). Number theorists are interested in classifying number fields whose symmetry groups (called Galois groups) have the commutative property, and in producing formulas to generate these special number fields. Modern methods have demonstrated the connection between number fields and certain associated functions called L-functions, whose values encode many of the most important conjectures in number theory. The principal investigator, Dr. Samit Dasgupta, has made important progress on these topics in recent work, and the current proposal aims to push further in this direction. Dr. Dasgupta also plans to continue and expand his activities to disseminate mathematics to students and academics of all age groups and career stages. Dr. Dasgupta gives expository lectures for undergraduates in various math clubs, teaches minicourses for graduate students, is involved in graduate and postdoctoral advising, is involved in local conference organizing, and is on the editorial board of several journals. All these activities connect to Dr. Dasgupta’s goal to promote mathematics holistically in society, with a particular view toward supporting various groups that have been traditionally underrepresented. More technically, Dr. Dasgupta’s work is motivated by two central problems in modern algebraic number theory: the expression of special values of classical and p-adic L-functions as regulators of algebraic objects, and the generation of abelian extensions of number fields through analytic means intrinsic to the ground field, as codified in Hilbert's 12th problem. Dr. Dasgupta’s prior work has made significant progress on the Brumer-Stark Conjecture, the Gross-Stark Conjecture, and the explicit analytic construction of class fields of totally real fields. Dr. Dasgupta will continue his explorations in this direction with five specific questions on the connections between Stark units, L-functions, modular forms, and Galois representations. All these projects will advance our knowledge in a significant way on the relationship between special values of L-functions and associated algebraic objects. Firstly, he will complete the proof of the Brumer-Stark conjecture by handling the localization at p=2. Next, he will extend his work with Kakde to prove the Equivariant Tamagawa Number Conjecture for the minus part of CM abelian extensions of totally real fields, including at the prime 2. In joint work with Spiess, Dr. Dasgupta will prove their joint conjecture on the characteristic polynomial of Gross's regulator matrix. Separately, he will work with Darmon and Charollois on expanding the strategy of Darmon, Vonk, and Pozzi for real quadratic fields to give a purely p-adic analytic proof of Dr. Dasgupta's explicit analytic formula for Brumer-Stark units over arbitrary totally real fields. Dr. Dasgupta will work with Victor Rotger to study a conjecture of Harris and Venkatesh relating the derived Hecke operators defined by Venkatesh to Stark units in the Galois extension cut out by the adjoint of the Galois representation attached to weight one forms.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.
这个项目涉及代数数论,它是数学的一个分支,旨在研究由多项式的根(称为数域)产生的基本数系的性质。数论家感兴趣的是对其对称群(称为伽罗瓦群)具有交换性质的数域进行分类,并给出生成这些特殊数域的公式。现代方法已经证明了数域和某些被称为L函数的相关函数之间的联系,这些函数的值编码了数论中许多最重要的猜想。首席研究员Samit Dasgupta博士在最近的工作中在这些专题上取得了重要进展,目前的提案旨在进一步推动这一方向。达斯古普塔博士还计划继续和扩大他的活动,向所有年龄段和职业阶段的学生和学者传播数学。达斯古普塔博士在不同的数学俱乐部为本科生讲授说明性课程,为研究生教授迷你课,参与研究生和博士后咨询,参与当地会议的组织,并是几家期刊的编辑委员会成员。所有这些活动都与达斯古普塔博士的目标有关,他的目标是在社会上全面推广数学,特别是支持传统上代表性不足的各种群体。更严格地说,达斯古普塔博士的工作是由现代代数数论中的两个核心问题推动的:经典的和p-进的L-函数作为代数对象的调节器的特定值的表达,以及通过基场固有的解析手段生成数域的阿贝尔扩张,如希尔伯特的第12个问题中所述。Dasgupta博士以前的工作在Brumer-Stark猜想、Gross-Stark猜想和全实域的类场的显式解析构造方面取得了重大进展。达斯古普塔博士将继续他在这个方向上的探索,提出五个关于斯塔克单位、L-函数、模形式和伽罗瓦表示之间的联系的具体问题。这些工作将极大地提高我们对L函数特殊值与相关代数对象之间关系的认识。首先,他将通过处理p=2的局部化来完成Brumer-Stark猜想的证明。接下来,他将扩展他与Kakde的工作,证明包括在素数2处的全实域的CM阿贝尔扩张的负部分的等变Tamagawa数猜想。在与Spiess的合作中,Dasgupta博士将证明他们关于Gross调节矩阵的特征多项式的联合猜想。另外,他将与Darmon和Charollois合作,将Darmon、Vonk和Pozzi的策略扩展到实二次域,以给出Dasgupta博士对任意全实域上Brumer-Stark单位的显式解析公式的纯p元解析证明。Dasgupta博士将与Victor Rotger一起研究Harris和Venkatesh的一个猜想,该猜想将由Venkatesh定义的派生Hecke算子与Galois扩展中的Stark单位相关联,该单位由附加在权重一形式上的Galois表示所切割。该奖项反映了NSF的法定使命,并已通过使用基金会的智力优势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)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Samit Dasgupta其他文献
The Eisenstein cocycle and Gross’s tower of fields conjecture
- DOI:
10.1007/s40316-015-0046-2 - 发表时间:
2016-01-07 - 期刊:
- 影响因子:0.400
- 作者:
Samit Dasgupta;Michael Spieß - 通讯作者:
Michael Spieß
A conjectural product formula for Brumer–Stark units over real quadratic fields
- DOI:
10.1016/j.jnt.2012.02.013 - 发表时间:
2013-03-01 - 期刊:
- 影响因子:
- 作者:
Samit Dasgupta - 通讯作者:
Samit Dasgupta
Samit Dasgupta的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Samit Dasgupta', 18)}}的其他基金
Beyond L-functions: the Eisenstein Cocycle and Hilbert's 12th Problem
超越 L 函数:爱森斯坦余循环和希尔伯特第 12 个问题
- 批准号:
1901939 - 财政年份:2019
- 资助金额:
$ 55万 - 项目类别:
Continuing Grant
CAREER: Explicit class field theory, Stark's conjectures, and families of modular forms
职业:显式类场论、斯塔克猜想和模块化形式族
- 批准号:
0952251 - 财政年份:2010
- 资助金额:
$ 55万 - 项目类别:
Continuing Grant
Gross-Stark units and p-adic families of Hilbert modular forms
希尔伯特模形式的 Gross-Stark 单位和 p-adic 系列
- 批准号:
0900924 - 财政年份:2009
- 资助金额:
$ 55万 - 项目类别:
Standard Grant
Gross-Stark units, Stark-Heegner points, and explicit class field theory for totally real fields
完全实数域的 Gross-Stark 单位、Stark-Heegner 点和显式类域论
- 批准号:
0901041 - 财政年份:2008
- 资助金额:
$ 55万 - 项目类别:
Standard Grant
Gross-Stark units, Stark-Heegner points, and explicit class field theory for totally real fields
完全实数域的 Gross-Stark 单位、Stark-Heegner 点和显式类域论
- 批准号:
0653023 - 财政年份:2007
- 资助金额:
$ 55万 - 项目类别:
Standard Grant
相似国自然基金
碱土金属原子ISO-→3PI和ISO→3P2跃迁多极和非线性Stark频移的理论研究
- 批准号:12404306
- 批准年份:2024
- 资助金额:30 万元
- 项目类别:青年科学基金项目
二维II-VI族半导体材料光学非线性和量子限域Stark效应机理研究及其应用
- 批准号:
- 批准年份:2021
- 资助金额:58 万元
- 项目类别:面上项目
基于新型光/电复合场制备高密度基态冷分子的Stark减速研究
- 批准号:12004199
- 批准年份:2020
- 资助金额:24.0 万元
- 项目类别:青年科学基金项目
基于三维能带调控的AlGaN基紫外LED量子限阈Stark效应研究
- 批准号:61974149
- 批准年份:2019
- 资助金额:60.0 万元
- 项目类别:面上项目
利用动态Stark效应对分子光化学反应的非绝热动力学研究
- 批准号:21773299
- 批准年份:2017
- 资助金额:64.0 万元
- 项目类别:面上项目
原子内轨道的反常动态STARK效应与干涉光电子谱
- 批准号:11674243
- 批准年份:2016
- 资助金额:57.0 万元
- 项目类别:面上项目
重原子极性分子的有效Stark减速与冷却及其eEDM精密测量
- 批准号:91536218
- 批准年份:2015
- 资助金额:360.0 万元
- 项目类别:重大研究计划
新颖高效静电Stark减速与囚禁方案的实验研究
- 批准号:11504112
- 批准年份:2015
- 资助金额:24.0 万元
- 项目类别:青年科学基金项目
非极性碘分子Rydberg-Stark减速和俘获
- 批准号:61575115
- 批准年份:2015
- 资助金额:63.0 万元
- 项目类别:面上项目
胶体量子点的电致发光和量子限制Stark效应
- 批准号:10774023
- 批准年份:2007
- 资助金额:42.0 万元
- 项目类别:面上项目
相似海外基金
Motional Stark effect (MSE) measurements of microwave-driven current profile on MAST-Upgrade
MAST-Upgrade 上微波驱动电流分布的动斯塔克效应 (MSE) 测量
- 批准号:
2888730 - 财政年份:2023
- 资助金额:
$ 55万 - 项目类别:
Studentship
SBIR Phase I: A Radio Frequency Quadrupole Stark Decelerator to Identify Isomers and Conformers and Measure their Effective Dipole Moments
SBIR 第一阶段:射频四极 Stark 减速器,用于识别异构体和构象异构体并测量其有效偶极矩
- 批准号:
2208750 - 财政年份:2023
- 资助金额:
$ 55万 - 项目类别:
Standard Grant
Multi-sensor Dean Stark alternative for online bitumen/solids/water estimation
用于在线沥青/固体/水估算的多传感器 Dean Stark 替代方案
- 批准号:
550316-2020 - 财政年份:2021
- 资助金额:
$ 55万 - 项目类别:
Alliance Grants
Development of spectroscopic diagnostic methods for magnetically confined plasmas using high sensitivity measurements of Stark and Zeeman effects
利用斯塔克效应和塞曼效应的高灵敏度测量开发磁约束等离子体的光谱诊断方法
- 批准号:
21H01054 - 财政年份:2021
- 资助金额:
$ 55万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Coherent Control of Cold Collision by Preparing Molecular Eigenstates Using Stark-Induced Adiabatic Passage
利用斯塔克诱导绝热通道制备分子本征态来相干控制冷碰撞
- 批准号:
2110256 - 财政年份:2021
- 资助金额:
$ 55万 - 项目类别:
Standard Grant
Spatial separation of molecular clusters by the Stark effect and its spectroscopic study
斯塔克效应分子簇的空间分离及其光谱研究
- 批准号:
20J01021 - 财政年份:2020
- 资助金额:
$ 55万 - 项目类别:
Grant-in-Aid for JSPS Fellows
Multi-sensor Dean Stark alternative for online bitumen/solids/water estimation
用于在线沥青/固体/水估算的多传感器 Dean Stark 替代方案
- 批准号:
550316-2020 - 财政年份:2020
- 资助金额:
$ 55万 - 项目类别:
Alliance Grants
Development of Stimulated Raman Stark Spectroscopy toward Space- and Time-Resolved Operando Analysis of Batteries
受激拉曼斯塔克光谱的发展,用于电池的空间和时间分辨操作分析
- 批准号:
19H02821 - 财政年份:2019
- 资助金额:
$ 55万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Euler Systems of Garrett-Rankin-Selberg type and Stark-Heegner points
Garrett-Rankin-Selberg 型和 Stark-Heegner 点的欧拉系统
- 批准号:
155499-2013 - 财政年份:2017
- 资助金额:
$ 55万 - 项目类别:
Discovery Grants Program - Individual