Conference: Arithmetic, Birational Geometry, and Moduli

该奖项为2023年6月12日至16日在布朗大学举行的“算术、双几何和模空间”会议提供支持。这次会议将把在代数几何领域工作的专家、早期研究人员和研究生联系起来。它的目标是鼓励该领域内的跨学科合作，并营造一个环境，使所有职业阶段的人都可以进行富有成效的互动。海报环节将重点介绍研究生和博士后的成果。会议结果将通过直播和视频档案传播。会议网址为https://sites.google.com/view/abgms2023/The，会议的技术重点将是解决奇点和半稳定减少。分解是指用重复爆破的光滑模型代替奇异代数变量。半稳定约简是寻找代数变种退化族的轻度奇异极限的密切相关的过程。这些是在模空间中构造二元模型和边界极限的基本工具。诸如代数堆栈、非阿基米德几何、对数几何和热带几何等新工具正在推动这些问题的进展。即使现有结果的证明变得更简单，新的、更强的解析和半稳定约简形式也在出现。这些发展为长期存在的算术问题提供了更深入的理解。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 provides support for the conference "Arithmetic, Birational Geometry, and Moduli Spaces" held at Brown University onJune 12-16, 2023. The conference will connect established experts, early career researchers, and graduate students working in algebraic geometry. Its goals are to encourage collaboration across sub-disciplines within the field and to foster an environment where people at all career stages may interact productively. A poster session will highlight achievements of graduate students and postdocs. Results of the meeting will be disseminated through live-streaming and video archives of lectures. The conference website is https://sites.google.com/view/abgms2023/The technical focus of the meeting will be resolution of singularities and semistable reduction. Resolution refers to the replacement of singular algebraic varieties with smooth models by repeated blowings up. Semistable reduction is the closely related process of finding mildly singular limits of degenerating families of algebraic varieties. These are fundamental tools for constructing birational models and boundary limits in moduli spaces. New tools like algebraic stacks, non-archimedean geometry, logarithmic geometry, and tropical geometry are driving progress on these questions. Novel, stronger forms of resolution and semistable reduction are appearing, even as the proofs of existing results become simpler. These developments offer a deeper understanding of long-standing arithmetic problems.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.