Trace Formulas and Relative Functoriality
迹公式和相对函数性
基本信息
- 批准号:1939672
- 负责人:
- 金额:$ 17.52万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2019
- 资助国家:美国
- 起止时间:2019-06-04 至 2022-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
In the 1960s mathematician Robert Langlands developed a vision connecting two apparently disparate fields of mathematics, number theory and representation theory. This work led to what is now known as the Langlands program, which reveals a web of deep and as yet only partially understood connections between number theory, representation theory, geometry, and mathematical physics. This project aims to answer core questions of the Langlands program revolving around the so-called functoriality conjecture, in a generalized setting known as the relative Langlands program. The relative Langlands program replaces reductive groups by more general homogeneous spaces, aiming to understand their local and automorphic spectra. A basic tool is the relative trace formula, a generalization of the Arthur-Selberg trace formula, which has still not been fully developed. The project aims to establish new types of comparisons between relative trace formulas that would simultaneously address the questions of relative functoriality, and of conjectural relations between periods of automorphic forms and L-functions. The two main goals of the project are: (1) the development of the technical basis for such comparisons, including a general relative trace formula, and (2) the development of a local-to-global strategy for the comparison of trace formulas, as in endoscopy, but with scalar transfer factors replaced by more general transfer operators.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.
在20世纪60年代,数学家罗伯特·朗兰兹(Robert Langlands)提出了一种观点,将数论和表示论这两个明显不同的数学领域联系起来。这项工作导致了现在被称为朗兰兹纲领的东西,它揭示了数论、表示论、几何和数学物理之间的一个深刻的、迄今为止只被部分理解的联系。该项目旨在回答朗兰兹纲领的核心问题,围绕所谓的功能性猜想,在一个广义的设置被称为相对朗兰兹纲领。 相对朗兰兹纲领用更一般的齐性空间取代约化群,旨在理解它们的局部和自守谱。一个基本的工具是相对迹公式,这是阿瑟-塞尔伯格迹公式的推广,它还没有得到充分的发展。该项目旨在建立新类型的比较相对迹公式,同时解决相对函性的问题,以及自守形式和L-函数的周期之间的关系。该项目的两个主要目标是:(1)发展这种比较的技术基础,包括一般相对痕量公式,和(2)发展局部到全局的痕量公式比较策略,如内窥镜检查,但标量转移因子被更一般的转移算子所取代。该奖项反映了NSF的法定使命,并被认为值得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。
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)
Transfer operators and Hankel transforms between relative trace formulas, I: Character theory
相对迹公式之间的传递算子和 Hankel 变换,I:特征理论
- DOI:10.1016/j.aim.2021.108010
- 发表时间:2022
- 期刊:
- 影响因子:1.7
- 作者:Sakellaridis, Yiannis
- 通讯作者:Sakellaridis, Yiannis
Functorial transfer between relative trace formulas in rank 1
1 阶相对迹公式之间的函数传递
- DOI:10.1215/00127094-2020-0046
- 发表时间:2021
- 期刊:
- 影响因子:2.5
- 作者:Sakellaridis, Yiannis
- 通讯作者:Sakellaridis, Yiannis
Intersection complexes and unramified ?-factors
交叉复合体和未分支的 ?-因子
- DOI:10.1090/jams/990
- 发表时间:2022
- 期刊:
- 影响因子:3.9
- 作者:Sakellaridis, Yiannis;Wang, Jonathan
- 通讯作者:Wang, Jonathan
Transfer operators and Hankel transforms between relative trace formulas, II: Rankin–Selberg theory
相对迹公式之间的传递算子和 Hankel 变换,II:Rankin-Selberg 理论
- DOI:10.1016/j.aim.2021.108039
- 发表时间:2022
- 期刊:
- 影响因子:1.7
- 作者:Sakellaridis, Yiannis
- 通讯作者:Sakellaridis, Yiannis
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Ioannis Sakellaridis其他文献
Ioannis Sakellaridis的其他文献
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{{ truncateString('Ioannis Sakellaridis', 18)}}的其他基金
Functoriality for Relative Trace Formulas
相对迹公式的函数性
- 批准号:
2401554 - 财政年份:2024
- 资助金额:
$ 17.52万 - 项目类别:
Continuing Grant
Geometric and Microlocal Study of Automorphic Periods
自守周期的几何和微局域研究
- 批准号:
2101700 - 财政年份:2021
- 资助金额:
$ 17.52万 - 项目类别:
Standard Grant
Trace Formulas and Relative Functoriality
迹公式和相对函数性
- 批准号:
1801429 - 财政年份:2018
- 资助金额:
$ 17.52万 - 项目类别:
Continuing Grant
Foundations of the Relative Langlands Program
相关朗兰兹纲领的基础
- 批准号:
1502270 - 财政年份:2015
- 资助金额:
$ 17.52万 - 项目类别:
Standard Grant
Spherical varieties in the Langlands program
朗兰兹计划中的球形品种
- 批准号:
1101471 - 财政年份:2011
- 资助金额:
$ 17.52万 - 项目类别:
Standard Grant
相似海外基金
Functoriality for Relative Trace Formulas
相对迹公式的函数性
- 批准号:
2401554 - 财政年份:2024
- 资助金额:
$ 17.52万 - 项目类别:
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还原代数群覆盖群的迹公式研究
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Computer Generation of Explicit Formulas for Jacobian Arithmetic on Hyperelliptic Curves
超椭圆曲线雅可比算术显式公式的计算机生成
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574796-2022 - 财政年份:2022
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Sampling discretization, cubature formulas and quantitative approximation in multidimensional settings
多维环境中的采样离散化、体积公式和定量近似
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RGPIN-2020-03909 - 财政年份:2022
- 资助金额:
$ 17.52万 - 项目类别:
Discovery Grants Program - Individual
Explicit Formulas for Functorial Transfer Kernels
函数传递核的显式公式
- 批准号:
547477-2020 - 财政年份:2022
- 资助金额:
$ 17.52万 - 项目类别:
Alexander Graham Bell Canada Graduate Scholarships - Doctoral
New developments in the anticyclotomic Iwasawa theory and special value formulas on L-functions
反圆剖分Iwasawa理论和L函数特殊值公式的新进展
- 批准号:
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- 资助金额:
$ 17.52万 - 项目类别:
Grant-in-Aid for Scientific Research (A)