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

杜克大学的 12 名教师组成的团队将领导一项长期的垂直整合培训计划，该计划足够强大，足以将学员发挥到最大潜力，并且足够灵活，可以容纳来自多个入门级别和学科领域焦点的学员。主要的培训结构是由教师领导的垂直整合的主题研究团队：这些团队将使各级学员接触到以数论为中心的相互关联的项目。每个专题研究团队将研究足够广泛和深入的问题，为博士后和研究生研究奠定基础，同时为本科生探索平台。专题研究团队将辅以七项举措，这些举措将促进本科生的研究参与和兴奋，加速和加强研究生研究和指导，加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，结合创新的招聘方法，建立专题研究团队。这些团队探索解析数论、调和分析、自同构形式、算术几何、p 进几何和同伦论等广泛的主题网络，所有这些主题都通过 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、混合具有不同研究兴趣的研究生的交叉培训项目、计算培训和教学法以及鼓励多样性的多个项目。 专题研究团队将同时培训新研究人员并开展前沿研究。 潜在的研究主题包括朗兰兹 L 函数的分析延拓、L 函数的特殊值以及与显式类域理论的联系、与动机同伦理论的联系以及簇上点的渐进性。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审查标准进行评估，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.