Conference: The Mordell conjecture 100 years later

该奖项将支持2024年7月8日至12日在麻省理工学院举行的名为《100年后的莫德尔猜想》的会议。会议的网站是https://mordell.org/，上面显示了被邀请的演讲者名单。1983年证明的莫德尔猜想是现代数论的里程碑之一。现在有必要就这一主题召开一次会议，因为近年来，关于这一猜想的不同方面已经取得了进展，而其他关键问题仍未解决。这将是第一次将来自这些不同视角的所有研究人员聚集在一起的会议。这次会议将有16个小时的演讲，演讲者从最初的专家到处于当前研究前沿的年轻数学家。一些讲座将以实地调查为特色，这对下一代研究人员特别具有教育价值。会议还将设有问题环节和许多5分钟的闪电演讲时段，这将使初级参与者有机会展示他们自己对各种相关主题的研究。该奖项将资助各种数学家的旅行和住宿，包括那些来自数学领域代表性不足的群体的人，以及来自其他资金来源不足的学院和大学的与会者。讲座、习题会议和闪电演讲的材料将在网站上公开提供，以接触到更广泛的受众，而不仅仅是会议与会者。莫德尔猜想推动了20世纪算术几何的发展，无论是在它被Faltings解决之前和之后。这次会议将以讲座为特色，涵盖与莫德尔猜想、其推广及其启发的其他工作相关的广泛主题。特别是，它将建立在以下方向的最新进展的基础上：1)Chabauty的p-进方法的非阿贝尔类似；2)最近通过p-进Hodge理论的证明；3)有理点数量的统一界限；4)通过各种方法研究的高维变体的推广：分析、上同调和计算。该奖项反映了NSF的法定使命，并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，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.