Conference: The Mordell conjecture 100 years later

该奖项将支持于2024年7月8日至12日在麻省理工学院举行的“100年后的莫德尔猜想”会议。会议的网站是https://mordell.org/，上面有受邀演讲者的名单。莫德尔猜想于1983年被证明，是现代数论的里程碑之一。现在需要召开一次关于这一主题的会议，因为近年来，在这一猜想的不同方面取得了进展，而其他关键问题仍未得到解决。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。会议将以16个小时的讲座为特色，演讲者既有原来的专家，也有处于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。会议还将设有一个问题讨论环节和许多5分钟的闪电演讲时段，这将使初级与会者有机会展示他们在各种相关主题上的研究成果。该奖项将支持各种数学家的旅行和住宿，包括那些来自数学领域代表性不足的群体的数学家，以及来自其他资金来源无法获得的学院和大学的与会者。讲座、问题讨论和闪电会谈的材料将在网站上公开，以接触到比会议参与者更广泛的受众。莫德尔猜想推动了20世纪算术几何的发展，无论是在法尔廷斯解决它之前还是之后。会议将以讲座为特色，涵盖与莫德尔猜想、它的概括以及它所启发的其他工作有关的广泛主题。特别是，它将建立在以下方向的最新进展：1)Chabauty的p进方法的非abel类似物；2) p进霍奇理论的最新证明；3)有理点数目的一致界；4)通过解析、上同调和计算等多种方法研究高维变量的推广。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。

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.