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

Duke University, Durham NC

Investigators

Abstract

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.