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

杜克大学的12名教师将领导一个长期的垂直整合培训计划，该计划足够强大，可以将学员提升到最高潜力，并且足够灵活，可以容纳来自多个入门级和学科领域的学员。主要的培训结构是教师领导的，垂直整合的专题研究团队：这些将使各级学员接触到以数论为中心的相互关联的项目。每个专题研究小组将调查的问题是广泛和深入的，足以形成博士后和研究生研究的基础，同时由本科生探索的平台。专题研究团队将补充七项举措，以促进本科生研究参与和兴奋，加速和加强研究生研究和指导，并加强博士后研究和专业发展。该项目利用高级人员的多元化专业知识，以及创新的招聘方法，建立专题研究团队。这些团队探索了解析数论，调和分析，自守形式，算术几何，p-adic几何和同伦理论中的广泛主题网络，所有这些都通过L-函数联系起来。创新的招聘方法包括千年问题课程，协作学习研讨会和讲习班，交叉培训计划混合研究生与不同的研究兴趣，计算培训和教学法，以及多个程序，以鼓励多样性。 专题研究小组将同时培训新的研究人员和执行尖端研究。 潜在的研究课题包括朗兰兹L-函数的解析延拓、L-函数的特殊值以及与显式类场论的联系、与运动同伦理论的联系以及簇上点的渐近性。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评审标准进行评估，被认为值得支持。

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.