RTG: Linked via L-functions: training versatile researchers across number theory

RTG：通过 L 函数链接：跨数论培训多才多艺的研究人员

• 批准号: 2231514
• 负责人: Heekyoung Hahn
• 金额: $ 250万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-10-01 至 2028-09-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2231514&HistoricalAwards=false
• 关键词: RTG; Linked; via; functions; training

A group of 12 faculty at Duke University will lead a long-lasting vertically-integrated training program that is strong enough to elevate trainees to their highest potential, and flexible enough to accommodate trainees from multiple entry-point levels and subject-area foci. The main training structure is faculty-led, vertically integrated Thematic Research Teams: these will expose trainees at all levels to inter-related projects centered in number theory. Each Thematic Research Team will investigate problems that are broad and deep enough to form a basis for postdoctoral and graduate research and simultaneously a platform for exploration by undergraduates. Thematic Research Teams will be supplemented with seven initiatives that will foster undergraduate research participation and excitement, accelerate and strengthen graduate research and mentoring, and enhance postdoctoral research and professional development.The project leverages the diverse expertise of the senior personnel, together with innovative recruitment methods, to build Thematic Research Teams. These teams explore a broad network of topics in analytic number theory, harmonic analysis, automorphic forms, arithmetic geometry, p-adic geometry, and homotopy theory, all linked via L-functions. The innovative recruitment methods include a Millennium Problems Course, collaborative learning seminars and workshops, cross-training programs mixing graduate students with different research interests, computational training and pedagogy, and multiple programs to encourage diversity. The Thematic Research Teams will simultaneously train new researchers and execute cutting edge research. Potential research topics include analytic continuation of Langlands L-functions, special values of L-functions and links to explicit class field theory, connections to motivic homotopy theory and asymptotics of points on varieties.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.

杜克大学（Duke University）的12名教职员工将领导一个持久的垂直综合培训计划，该计划足以将学员提升到他们的最高潜力，并且足够灵活，可以容纳来自多个入口点和主题区域焦点的受训者。主要的培训结构是教师主导的，垂直综合的主题研究团队：这些将使各级受训人员接触到以数字理论为中心的相关项目。每个主题研究团队都将调查足够广泛且深入的问题，以构成博士后研究和研究生研究的基础，并同时通过本科生进行探索平台。主题研究团队将为七项举措提供补充，这些举措将促进本科研究的参与和兴奋，加速和加强研究生研究和指导，并增强博士后研究和专业发展。该项目利用高级人员的多样化专业知识，以及创新的招聘方法，以建立主题研究团队。这些团队探索了分析数理论，谐波分析，自身形式，算术几何形状，P-ADIC几何形状和同义理论的广泛主题网络，这些网络都是通过L功能链接的。创新的招聘方法包括千年问题课程，协作学习研讨会和研讨会，交叉培训计划，将研究生具有不同的研究兴趣，计算培训和教学法以及鼓励多样性的多个计划。 主题研究团队将同时培训新的研究人员并执行尖端研究。 潜在的研究主题包括Langlands L功能的分析性延续，L功能的特殊价值以及与显式阶级现场理论的联系，与动机同型理论的联系以及品种上的渐进点的联系。该奖项反映了NSF的法定任务，并认为通过基金会的知识绩效和广泛的crietia crietia cripitia cripitia cripitia cripitia cripitia criperia cripitia cripitia cripitia cripitia cripitia cripitia cripitia cripitia recteria the Croperia rection the奖项。