Parahoric Character Sheaves and Representations of p-Adic Groups
隐喻特征束和 p-Adic 群的表示
基本信息
- 批准号:2401114
- 负责人:
- 金额:$ 33万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2024
- 资助国家:美国
- 起止时间:2024-07-01 至 2027-06-30
- 项目状态:未结题
- 来源:
- 关键词:
项目摘要
In the past half century, cutting-edge discoveries in mathematics have occurred at the interface of three major disciplines: number theory (the study of prime numbers), representation theory (the study of symmetries using linear algebra), and geometry (the study of solution sets of polynomial equations). The interactions between these subjects has been particularly influential in the context of the Langlands program, arguably the most expansive single project in modern mathematical research. The proposed research aims to further these advances by exploring geometric techniques in representation theory, especially motivated by questions within the context of the Langlands conjectures. This project also provides research training opportunities for undergraduate and graduate students.In more detail, reductive algebraic groups over local fields (local groups) and their representations control the behavior of symmetries in the Langlands program. This project aims to develop connections between representations of local groups and two fundamental geometric constructions: Deligne-Lusztig varieties and character sheaves. Over the past decade, parahoric analogues of these geometric objects have been constructed and studied, leading to connections between (conjectural) algebraic constructions of the local Langlands correspondence to geometric phenomena, and thereby translating open algebraic questions to tractable problems in algebraic geometry. In this project, the PI will wield these novel positive-depth parahoric analogues of Deligne-Lusztig varieties and character sheaves to attack outstanding conjectures in the local Langlands program.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.
在过去的半个世纪里,数学的前沿发现发生在三个主要学科的交界处:数论(研究素数),表示论(使用线性代数研究对称性)和几何学(研究多项式方程的解集)。这些学科之间的相互作用在朗兰兹纲领的背景下特别有影响力,可以说是现代数学研究中最广泛的单一项目。拟议中的研究旨在通过探索表征理论中的几何技术来进一步推进这些进展,特别是朗兰兹结构背景下的问题。该项目还为本科生和研究生提供了研究培训的机会。更详细地说,局部域上的约化代数群(局部群)及其表示控制了Langlands程序中对称性的行为。这个项目的目的是发展本地群体的表示和两个基本的几何结构之间的联系:Deligne-Lusztig品种和字符层。在过去的十年中,这些几何对象的parahoric类似物已被构建和研究,导致连接的局部朗兰兹对应几何现象的代数结构之间的连接,从而将开放的代数问题转化为代数几何中的易处理的问题。在这个项目中,PI将运用Deligne-Lusztig品种和字符束的这些新颖的正深度parahoric类似物来攻击当地Langlands计划中的杰出成果。这个奖项反映了NSF的法定使命,并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,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)
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Charlotte Chan其他文献
Representation theory of finite groups
有限群表示论
- DOI:
10.1017/9781316856383.011 - 发表时间:
2011 - 期刊:
- 影响因子:0
- 作者:
Charlotte Chan;Martin Isaacs;Peter Hermann - 通讯作者:
Peter Hermann
A Throat Lozenge Containing Amyl Meta Cresol and Dichlorobenzyl Alcohol Has a Direct Virucidal Effect on Respiratory Syncytial Virus, Influenza a and SARS-CoV
含有戊基间甲酚和二氯苯甲醇的润喉糖对呼吸道合胞病毒、甲型流感和 SARS-CoV 有直接杀病毒作用
- DOI:
- 发表时间:
2005 - 期刊:
- 影响因子:0
- 作者:
J. Oxford;R. Lambkin;I. Gibb;S. Balasingam;Charlotte Chan;A. Catchpole - 通讯作者:
A. Catchpole
The scalar product formula for parahoric Deligne--Lusztig induction
平行德利涅的标量积公式--Lusztig归纳
- DOI:
10.1215/00127094-2022-0080 - 发表时间:
2024 - 期刊:
- 影响因子:2.5
- 作者:
Charlotte Chan - 通讯作者:
Charlotte Chan
‘I thought we would be nourished here’: The complexity of nutrition/food and its relationship to mental health among Arab immigrants/refugees in Canada: The CAN-HEAL study
“我以为我们会在这里得到滋养”:加拿大阿拉伯移民/难民营养/食物的复杂性及其与心理健康的关系:CAN-HEAL 研究
- DOI:
10.1016/j.appet.2024.107226 - 发表时间:
2024 - 期刊:
- 影响因子:5.4
- 作者:
Sarah Elshahat;Tina Moffat;Basit Kareem Iqbal;K. B. Newbold;Olivia Gagnon;Haneen Alkhawaldeh;Mahira Morshed;Keon Madani;Mafaz Gehani;Tony Zhu;Lucy Garabedian;Yasmine Belahlou;Sarah A.H. Curtay;Irene Hui;Charlotte Chan;Deniz Duzenli;Nathasha Rajapaksege;Bisma Shafiq;Amna Zaidi - 通讯作者:
Amna Zaidi
Charlotte Chan的其他文献
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{{ truncateString('Charlotte Chan', 18)}}的其他基金
Geometric Methods in Representation Theory and the Langlands Program
表示论中的几何方法和朗兰兹纲领
- 批准号:
2101837 - 财政年份:2021
- 资助金额:
$ 33万 - 项目类别:
Continuing Grant
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