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

这个CNIC提案旨在支持巴克内尔大学的Nathan Ryan博士及其合作者阿根廷布宜诺斯艾利斯大学的Ariel Pacetti博士、乌拉圭Republicica大学的Gonzalo Tornaria博士和智利圣地亚哥智利大学的Yves Martin博士之间关于高阶模形式的理论和计算研究。 模形式是数论中的一个重要课题。 在怀尔斯证明费马之后？的最后定理在九十年代，许多工作的基础和计算性质，导致了一个相当完整的理解之间的关系模形式的秩一，椭圆曲线，和他们的L-功能。 PI和他的合作者希望将这种理解扩展到更高级别的模块形式。 每个合作者都为项目带来了不同的专业知识，因此他们将能够处理许多不同的方法和主题。 他们还将试图通过北美和南美研究人员之间的联系传播和推进模块化形式的研究，并将来自美国历史上代表性不足的群体的三名研究生与乌拉圭的同行进行互动，同时参与与排名大于1的模块化形式有关的计算和理论研究项目。

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.