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

杜克大学（Duke University）的12名教员将领导一个长期的垂直整合培训项目，该项目足够强大，足以提升学员的最大潜力，并足够灵活，以适应来自多个入门级和学科领域重点的学员。主要的培训结构是教师主导的，垂直整合的专题研究小组：这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研究足够广泛和深入的问题，以形成博士后和研究生研究的基础，同时成为本科生探索的平台。专题研究小组将辅以七项举措，以促进本科生的研究参与和兴奋，加快和加强研究生的研究和指导，并加强博士后的研究和专业发展。该项目利用高级人才的多样化专业知识，结合创新的招聘方法，建立专题研究团队。这些团队探索了解析数论、调和分析、自同构形式、算术几何、p进几何和同伦理论等广泛的主题网络，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、合作学习研讨会和讲习班、交叉培训项目，将具有不同研究兴趣的研究生混合在一起，计算培训和教学法，以及鼓励多样性的多个项目。专题研究小组将同时培训新的研究人员并开展前沿研究。潜在的研究课题包括Langlands l -函数的解析延拓、l -函数的特殊值及其与显式类场论的联系、与动机同伦理论的联系以及变异点的渐近性。该奖项反映了美国国家科学基金会的法定使命，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。

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.