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，双有理几何和模空间”会议提供支持。会议将连接既定的专家，早期的职业研究人员和研究生在代数几何工作。它的目标是鼓励跨领域内的子学科的合作，并培养一个环境，在所有职业阶段的人可以进行有效的互动。海报会议将突出研究生和博士后的成就。会议成果将通过直播和讲座视频档案传播。会议的网站是https://sites.google.com/view/abgms2023/The会议的技术重点将是奇异性和半稳定约化的解决方案。归结是指通过反复的爆破将奇异代数簇替换为光滑模型。半稳定约化是与寻找退化代数簇族的轻度奇异极限密切相关的过程。这些是在模空间中构造双有理模型和边界极限的基本工具。新的工具，如代数堆栈，非阿基米德几何，对数几何和热带几何正在推动这些问题的进展。新的，更强的形式的决议和半稳定的减少出现，即使现有的结果变得更简单的证明。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。

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.