Number Theory: From Arithmetic Statistics to Zeta Elements II

Dartmouth College, Hanover NH

Investigators

Abstract

This travel grant will help bring junior US mathematicians (students, postdoctoral fellows, and other young researchers with limited access to resources) to the Centre de Recherches Mathematiques (CRM) in Montreal to participate in three workshops in winter 2015 on the following topics: * regulators, Mahler measures, and special values of L-functions (February 16-20, 2015); * p-adic methods in the theory of classical automorphic forms (March 9-14, 2015); and * the Kudla programme (April 6-10, 2015). These subjects are of great current interest in number theory, and these meetings will present opportunities for young US researchers to interact with leading researchers in the field. Talks and presentations will be made accessible to students and recent doctoral degree recipients who are relatively new to the subjects. Their participation will further existing relationships between researchers in the US and Canada. The past two decades have seen a wealth of new and exciting developments related to number theory, including: * striking progress on the Birch and Swinnerton-Dyer conjecture; * proofs of the Shimura-Taniyama-Weil conjecture, Serre's conjectures, the Fontaine-Mazur conjecture for two-dimensional Galois representations, and the Sato-Tate conjectures; * revolutionary ideas blending techniques in harmonic analysis and additive combinatorics, and a breakthrough on primes in arithmetic progressions; * new interpretations of algebraic objects and consequences for ranks of elliptic curves and points on higher genus curves; * great progress in establishing bounds on gaps between primes. The CRM thematic year "Number Theory: From Arithmetic Statistics to Zeta Elements" is intended to broaden the impact of these spectacular results to a wide community and to develop the connections between them; this series of conferences will broaden participation by young participants and encourage them to build connections with people from all over the world. The February conference "Regulators, Mahler Measures, and Special Values of L-Functions" concerns the intriguing identities relating these topics (http://www.crm.umontreal.ca/2015/Mahler15/index_e.php). The March conference "p-Adic Methods in the Theory of Classical Automorphic Forms" is on p-adic methods and the theory of Galois representations, families of automorphic forms, p-adic Hodge theory, and the Langlands program (http://www.crm.umontreal.ca/2015/Automorph15/index_e.php). Finally, the April conference "The Kudla Programme" treats the latest developments stemming from the ideas relating the Fourier coefficients of central derivatives of incoherent Siegel Eisenstein series to arithmetic intersections of special cycles on unitary and orthogonal Shimura varieties (http://www.crm.umontreal.ca/2015/Kudla15/index_e.php).