US collaboration with Argentina, Chile, and Uruguay: Modular Forms in the Southern Cone

Bucknell University, Lewisburg PA

Investigators

Abstract

This CNIC proposal aims to support research between Dr. Nathan Ryan of Bucknell University and his collaborators, Dr. Ariel Pacetti of the Universidad de Buenos Aires, Argentina, Dr. Gonzalo Tornaria of the Universidad de la Republica in Uruguay, and Dr. Yves Martin of the Universidad de Chile, in Santiago, Chile, on the theoretical and computational study of modular forms of higher rank. Modular forms are an important subject within number theory. After Andrew Wiles proved Fermat?s Last Theorem in the nineties, much work of foundational and computational nature has led to a fairly complete understanding of the relationships between modular forms of rank one, elliptic curves, and their L-functions. The PI and his collaborators would like to extend that understanding to modular forms of higher rank. Each of the collaborators brings different expertise to the project and thus they will be able to tackle a number of different approaches and topics. They will also attempt to disseminate and advance the study of modular forms through contacts between researchers in the area from North and South America and by bringing three graduate students from historically underrepresented groups from the United States to interact with their peers in Uruguay, while involved in computational and theoretical research projects related to modular forms of rank greater than one.