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日在台湾台北国立台湾大学校园内的国家理论科学中心（NCTS）举行的函数场算术和丢番图几何会议。 会议的目的是汇集来自地球仪的数论研究人员，特别是函数场算术，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20名受邀演讲者，从著名的数学家到最近的博士。的日程安排将包括6-8个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.自从上世纪Artin和Weil的早期工作以来，人们已经知道，正特征的有限域上的代数曲线的函数域的研究与数域的研究非常相似。 与此同时，丢番图几何也适用于技术从代数几何问题的数论，因此这两个主题是密切交织在一起，努力解决深层次问题的数论使用几何方法。 会议将重点关注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，包括模块化形式和伽罗瓦表示，L函数的特殊值，算术动力学和品种上的合理点。 这些主题是数论研究的前沿，近年来在这些领域取得了一些重大进展。 该会议将为与会者提供与更广泛的数学界交流他们的研究的机会，并启动新的研究项目，推进数论的这些重要领域。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.