权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Trace Formulas and Relative Functoriality

迹公式和相对函数性

基本信息

批准号：
1801429
负责人：
Ioannis Sakellaridis
金额：
$ 21万
依托单位：
Rutgers University Newark
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-07-01 至 2019-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1801429&HistoricalAwards=false
关键词：
Trace Formulas Relative Functoriality

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.

20 世纪 60 年代，数学家罗伯特·朗兰兹 (Robert Langlands) 提出了一种将数论和表示论这两个看似不同的数学领域联系起来的愿景。这项工作导致了现在所谓的朗兰兹计划，该计划揭示了数论、表示论、几何和数学物理之间的深刻但迄今为止仅部分被理解的联系。该项目旨在在称为相对朗兰兹纲领的广义环境中回答围绕所谓函子性猜想的朗兰兹纲领的核心问题。相关的朗兰兹纲领用更一般的齐次空间取代了还原群，旨在理解它们的局部谱和自同构谱。一个基本工具是相对迹公式，它是 Arthur-Selberg 迹公式的推广，但尚未完全开发出来。该项目旨在建立相对迹公式之间的新型比较，同时解决相对函子性问题以及自守形式和 L 函数周期之间的猜想关系问题。该项目的两个主要目标是：(1) 开发此类比较的技术基础，包括通用相对迹线公式，以及 (2) 开发用于比较迹线公式的局部到全局策略，如内窥镜检查，但用更通用的传输算子取代标量传输因子。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查进行评估，被认为值得支持标准。