Arithmetic of Function Fields and Diophantine Geometry

该奖项支持来自美国机构的数学家参加将于2019年5月20日至24日在台北国立台湾大学校园国家理论科学中心（NCTS）举行的“函数场算术与丢番图几何”会议。会议的目的是汇集来自世界各地的数论研究人员，特别是函数域算术、丢番图几何和相关领域的研究人员。主要目标将是讨论这些领域的最新进展，并鼓励进一步的研究和未来的合作，会议的一个重要方面将是增加初级研究人员的参与。除了邀请20位来自知名数学家和新近获得博士学位的演讲者外，该计划还将包括6-8位由研究生和博士后研究人员贡献的演讲。会议网址为http://www.ncts.ntu.edu.tw/events_2_detail.php?nid=216.Since Artin和Weil在上个世纪的早期工作，众所周知，有限域上正特征代数曲线的函数场的研究与数域的研究有着密切的相似之处。同时，丢芬图几何也将代数几何的技术应用于数论问题，因此这两个学科在用几何方法解决数论中的深层问题方面是紧密交织在一起的。会议将集中讨论函数域算术和丢番图几何的各个方面，这些方面加强了共同的观点，并为思想的交叉授粉提供了机会，包括模形式和伽罗瓦表示、l函数的特殊值、算术动力学和变种上的有理点。这些主题是数论研究的前沿，近年来在这些领域取得了几项重大进展。会议将为参与者提供机会与更广泛的数学界交流他们的研究，并发起新的研究项目，以推进数论的这些重要领域。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award supports mathematicians from US institutions to participate at the conference Arithmetic of Function Fields and Diophantine Geometry, to be held on May 20-24, 2019, at the National Center for Theoretical Sciences (NCTS) on the campus of National Taiwan University in Taipei, Taiwan. The purpose of the conference will be to bring together both established and junior researchers in Number Theory from across the globe, and especially researchers in Function Field Arithmetic, Diophantine Geometry, and related fields. Primary goals will be to discuss recent advances in these areas and to encourage further research and future collaboration, and one important aspect of the conference will be to increase participation of junior researchers. In addition to twenty invited speakers ranging from established mathematicians to recent Ph.D.'s, the schedule will include 6-8 contributed talks by graduate students and post-doctoral researchers. The conference website is http://www.ncts.ntu.edu.tw/events_2_detail.php?nid=216.Since early work of Artin and Weil in the last century, it has been known that the study of function fields of algebraic curves over finite fields in positive characteristic runs in close analogy with the study of number fields. At the same time Diophantine geometry also applies techniques from algebraic geometry to problems in number theory, and so the two subjects are closely intertwined in their efforts to resolve deep problems in number theory using geometric methods. The conference will focus on aspects of function field arithmetic and Diophantine geometry that strengthen common points of view and present opportunities for cross-pollination of ideas, including modular forms and Galois representations, special values of L-functions, arithmetic dynamics, and rational points on varieties. These topics are on the forefront of research in Number Theory, and there have been several major advances in these areas in recent years. The conference will afford participants the opportunities to communicate their research with a broader mathematical community and to initiate new research projects that advance these important areas of Number Theory.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.