Trace Formulas and Relative Functoriality

迹公式和相对函数性

• 批准号: 1939672
• 负责人: Ioannis Sakellaridis
• 金额: $ 17.52万
• 依托单位: Johns Hopkins University
• 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: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1939672&HistoricalAwards=false
• 关键词: Trace; Formulas; Relative; Functoriality; Trace; Formulas; Relative; Functoriality

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1960年代，数学家罗伯特·兰兰兹（Robert Langlands）建立了一个愿景，该愿景连接了两个明显不同的数学领域，数字理论和代表理论。这项工作导致了现在所谓的兰兰兹计划，该计划揭示了一个深厚的网络，但尚未部分理解数字理论，表示理论，几何和数学物理学之间的联系。该项目旨在在称为相对兰兰兹计划的广义环境中回答围绕所谓功能性猜想的兰兰兹计划的核心问题。 相对的兰兰兹计划用更一般的均匀空间取代了还原群，旨在了解其本地和自动形态光谱。一个基本的工具是相对痕迹公式，这是Arthur-Selberg痕量公式的概括，该公式仍未得到充分发展。该项目旨在在相对痕量公式之间建立新类型的比较，这些公式将同时解决相对功能的问题，以及自动形式和L功能时期之间的猜想。该项目的两个主要目标是：（1）进行此类比较的技术基础，包括广义相对痕量公式，以及（2）在内窥镜检查中的局部到全球策略的制定，用于比较痕量公式，但标量转移因子被更广泛的传统奖励依据。通过更广泛的构建奖励，该奖项通过构建的构建范围来构建，这是众所周知的范围。 标准。