Trace Formula, Analytic Number Theory, and Langlands Functoriality

迹公式、解析数论和朗兰兹函子性

基本信息

  • 批准号:
    1702176
  • 负责人:
  • 金额:
    $ 17.35万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2017
  • 资助国家:
    美国
  • 起止时间:
    2017-07-01 至 2020-06-30
  • 项目状态:
    已结题

项目摘要

The Langlands Program, dating back to the letter written by R. P. Langlands to A. Weil in 1967, predicts surprising connections between arithmetic (e.g. properties of solutions to polynomial equations) and analysis (e.g., highly symmetric solutions to certain differential equations on symmetric manifolds (i.e.,automorphic forms)). The "Functoriality Conjectures" lie at the heart of the Langlands program. These are deep conjectures having far-reaching consequences both in number theory and the theory of automorphic forms. For instance, the celebrated proof of Fermat's Last Theorem by A. Wiles uses a case of functoriality conjectures proved earlier by Langlands and Tunnell. Although significant progress has been made towards these conjectures, in their utmost generality they are wide open. This research project aims to develop tools and techniques to prove further cases of functoriality conjectures. One of the most general and power tools in the theory of automorphic forms is the Arthur-Selberg trace formula. It has been successfully used in proving cases of functoriality conjectures. In all of these cases it is a comparison between two different trace formulas that was utilized. In a recent proposal called "Beyond Endoscopy" Langlands proposed a new approach to attack the functoriality conjectures in general. It is a fundamentally new approach aiming to analyze poles of automorphic L-functions using the trace formula and, in particular, is non-comparative. There are various difficulties, intrinsic to the discrete part of the trace formula, that need to be addressed before utilizing it in Beyond Endoscopy. This aim of this project is twofold: First is to address these difficulties in the case of GL(N) (following PI's earlier works and suggestions of Arthur) and get an explicit trace formula on the cuspidal part of the spectrum. The second goal is to use the resulting formula to execute Beyond Endoscopy for various automorphic L-functions.
朗兰兹计划,可以追溯到R.P.朗兰兹1967年写给A.Weil的信,它预测了算术(例如,多项式方程的解的性质)和分析(例如,对称流形上的某些微分方程解的高度对称解(即,自同构形式))之间惊人的联系。“函数性猜想”是朗兰兹计划的核心。这些都是深刻的猜想,在数论和自同构形式理论中都有深远的后果。例如,A.Wiles著名的费马大定理证明使用了早些时候由朗兰兹和图内尔证明的函数性猜想的情况。尽管在这些猜想方面已经取得了重大进展,但总的来说,这些猜想是完全开放的。这个研究项目的目的是开发工具和技术来证明函数性猜想的进一步情况。自同构形理论中最通用和最强大的工具之一是Arthur-Selberg迹公式。它已成功地用于证明函数性猜想的情形。在所有这些情况下,使用的是两个不同的示踪公式之间的比较。在最近一项名为“超越内窥镜”的提案中,朗兰兹提出了一种新的方法,从总体上攻击功能性猜想。利用迹公式分析自同构L函数的极点是一种全新的方法,特别是它具有非比较性。在超越内窥镜检查中使用跟踪公式的离散部分之前,需要解决各种固有的困难。这个项目的目的有两个:首先是解决GL(N)的这些困难(遵循Pi的早期工作和Arthur的建议),并得到关于谱的尖端部分的显式迹公式。第二个目标是使用得到的公式为各种自同构L函数执行Beyond内窥镜。

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 }}

Salim Altug其他文献

Salim Altug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 }}

相似海外基金

Should infant formula be available at UK food banks? Evaluating different pathways to ensuring parents in financial crisis can access infant formula.
英国食品银行应该提供婴儿配方奶粉吗?
  • 批准号:
    MR/Z503575/1
  • 财政年份:
    2024
  • 资助金额:
    $ 17.35万
  • 项目类别:
    Research Grant
Infant formula: Alternative protein study and regulatory roadmap
婴儿配方奶粉:替代蛋白质研究和监管路线图
  • 批准号:
    10108649
  • 财政年份:
    2024
  • 资助金额:
    $ 17.35万
  • 项目类别:
    Collaborative R&D
Assessment of Early Life PFAS Exposure in Perinatal Biospecimens, Infant Formula, and Breastmilk.
围产期生物样本、婴儿配方奶粉和母乳中生命早期 PFAS 暴露的评估。
  • 批准号:
    10723660
  • 财政年份:
    2023
  • 资助金额:
    $ 17.35万
  • 项目类别:
Analogues of the Weierstrass representation formula and extension problem of submanifolds at their singularities
Weierstrass 表示公式的类似物和奇点处子流形的可拓问题
  • 批准号:
    22H01121
  • 财政年份:
    2022
  • 资助金额:
    $ 17.35万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Development of Thermal Contact Resistance Prediction Formula Considering Details of Heat Transport Phenomena in Solid-Solid Contact Surface
考虑固-固接触表面传热现象细节的热接触热阻预测公式的开发
  • 批准号:
    22K03949
  • 财政年份:
    2022
  • 资助金额:
    $ 17.35万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Construction of salt permeation prediction formula for concrete structures with continuous or repetitive compressive stress
连续或重复压应力混凝土结构盐渗透预测公式的构建
  • 批准号:
    22K04290
  • 财政年份:
    2022
  • 资助金额:
    $ 17.35万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
The Verbatim Formula: Sometimes a Hug Goes a Long Way
逐字公式:有时一个拥抱会带来很大的帮助
  • 批准号:
    AH/V008579/1
  • 财政年份:
    2022
  • 资助金额:
    $ 17.35万
  • 项目类别:
    Research Grant
Beyond Endoscopy and the stable trace formula
超越内窥镜检查和稳定的痕量公式
  • 批准号:
    RGPIN-2020-04547
  • 财政年份:
    2022
  • 资助金额:
    $ 17.35万
  • 项目类别:
    Discovery Grants Program - Individual
The Satake transform and the trace formula
Satake变换和迹公式
  • 批准号:
    RGPIN-2017-03784
  • 财政年份:
    2021
  • 资助金额:
    $ 17.35万
  • 项目类别:
    Discovery Grants Program - Individual
Class number formula over global field of characteristic p and with coefficients.
特征 p 和系数的全局域上的类数公式。
  • 批准号:
    21K03186
  • 财政年份:
    2021
  • 资助金额:
    $ 17.35万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了