Conference: Arithmetic Cycles, Modular Forms, and L-functions

This award provides support for US-based students and early-career researchers to participate the conference "Arithmetic cycles, Modular forms, and L-functions" that will take place at the Centre de Recherches Mathématiques (CRM) in Montréal, August 18-22, 2025. The scientific program of the conference will revolve around recent advances in Number Theory and Arithmetic Geometry. A focus will be on novel uses of p-adic analytic methods to the study of algebraic problems, such as the construction of rational points on elliptic curves (a problem at the core of Birch–Swinnerton-Dyer conjecture, one of the Millenium Prize Problems by the Clay Mathematics Institute) and the construction of class fields of totally real fields (a salient case of Hilbert’s 12th problem from his 1900 ICM address). With the novel use of p-adic methods as an overarching theme, the scientific program of the conference will revolve around the latest advancements in some of the deepest and most exciting directions in Number Theory and Arithmetic Geometry, including: arithmetic cycles and special values of L-functions, and their link with Iwasawa theory, with new applications to the Birch–Swinnerton-Dyer conjecture and the Bloch–Kato conjectures; Stark’s conjectures, with a focus on its p-adic analogues and its elliptic analogues; and the emerging p-adic Kudla program and its role in an eventual analogue for totally real fields of the classical theory of Complex Multiplication. Conference webpage: https://www.eventcreate.com/e/darmonfest 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.