Conference: The Mordell conjecture 100 years later

该奖项将支持一个会议，“莫德尔猜想100年后”，在马萨诸塞州理工学院在一周7月8日至12日，2024年。 会议的网站是https://mordell.org/，上面有受邀发言者的名单。 1983年证明的莫德尔猜想是现代数论的里程碑之一。 现在需要召开一次关于这个主题的会议，因为近年来，在猜想的不同方面都取得了进展，而其他关键问题仍然没有解决。 这将是第一次将来自这些不同观点的所有研究人员聚集在一起的会议。 会议将有16个小时的讲座，演讲者从最初的专家到当前研究前沿的年轻数学家。 一些讲座将以该领域的调查为特色，特别是对下一代研究人员具有教育价值。 会议还将包括一个问题环节和许多5分钟的闪电谈话时段，这将为初级参与者提供展示他们自己对各种相关主题的研究的机会。 该奖项将支持各种数学家的旅行和住宿，包括那些来自数学代表性不足的群体和来自其他资金来源不可用的学院和大学的与会者。 从讲座，问题会议，和闪电会谈的材料将在网站上公开，以达到更广泛的观众不仅仅是会议的与会者。莫德尔猜想的动机很大的发展算术几何在20世纪，无论是之前和之后的决议，由Faltings。 会议将以讲座为特色，涵盖了与莫德尔猜想，其推广和其他工作，它启发了广泛的主题。 特别是，它将建立在以下方向的最新进展：1）Chabauty的p-adic方法的nonabelian类似物; 2）最近通过p-adic Hodge理论的证明; 3）有理数点的数量上的一致界限; 4）通过各种方法研究的高维变种的推广：该奖项反映了NSF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。

The award will support a conference, ``The Mordell conjecture 100 years later'', at the Massachusetts Institute of Technology during the week July 8-12, 2024. The conference website, showing the list of invited speakers, is https://mordell.org/ . The Mordell conjecture, proved in 1983, is one of the landmarks of modern number theory. A conference on this topic is needed now, because in recent years, there have been advances on different aspects of the conjecture, while other key questions remain unsolved. This would be the first conference to bring together all the researchers coming from these different perspectives. The conference will feature 16 hour-long lectures, with speakers ranging from the original experts to younger mathematicians at the forefront of current research. Some lectures will feature surveys of the field, which have educational value especially for the next generation of researchers. The conference will also feature a problem session and many 5-minute lightning talk slots, which will give junior participants an opportunity to showcase their own research on a wide variety of relevant topics. The award will support the travel and lodging of a variety of mathematicians including those from underrepresented groups in mathematics and attendees from colleges and universities where other sources of funding are unavailable. Materials from the lectures, problem session, and lightning talks will be made publicly available on the website, to reach an audience broader than just conference attendees.The Mordell conjecture motivated much of the development of arithmetic geometry in the 20th century, both before and after its resolution by Faltings. The conference will feature lectures covering a broad range of topics connected with the Mordell conjecture, its generalizations, and other work it has inspired. In particular, it will build on recent advances in the following directions: 1) nonabelian analogues of Chabauty's p-adic method; 2) the recent proof via p-adic Hodge theory; 3) uniform bounds on the number of rational points; 4) generalizations to higher-dimensional varieties, studied by various methods: analytic, cohomological, and computational.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.