Southwest Conference on Arithmetic Geometry

西南算术几何学术会议

• 批准号: 2200721
• 负责人: Brandon Levin
• 金额: $ 44.84万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-09-01 至 2025-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2200721&HistoricalAwards=false
• 关键词: Southwest; Conference; Arithmetic; Geometry

With support from this award, the Southwest Center for Arithmetic Geometry will continue its series of annual "Winter Schools" from 2023 to 2025 at the University of Arizona in Tucson, AZ, the first taking place March 4-8, 2023. Since its founding in 1997, the primary activity of the Southwest Center is the Arizona Winter School (AWS), an annual meeting which has become a prominent national event and provides high-level training and research experience for graduate students in arithmetic geometry and related areas. The AWS is organized around a different central topic each year and features a set of courses and accompanying research projects carefully designed and delivered by leading and emerging experts. The result is a unique fusion of traditional mathematics conference and intensive research workshop: the speakers organize courses of four or five lectures and propose research projects for graduate students to work on during the meeting. Nightly working sessions on these projects and on separate problem sets are run by the speakers and postdoctoral fellows. On the last day, students present their findings to the participants of the meeting. The result is a particularly intense and focused five days of mathematical activity for everyone involved. This cycle the Southwest Center will expand its programming to include Preliminary Arizona Winter School (PAWS). This virtual program aimed at advanced undergraduates and junior graduate students from underrepresented groups will feature two six-week-long courses during the fall semester organized around the same topic as the AWS. Participants will engage in weekly problem sessions run by advanced graduate students and participate in community building and mentorship activities. At both AWS and PAWS, connections among peers are formed, and mentoring relationships between students and senior researchers are developed. Subsequent collaborations between participants at all levels are the norm. Students make concrete strides toward becoming research mathematicians, post-doctoral assistants gain valuable mentoring experience in their academic careers, and faculty develop new interests and see new connections that lead to important published results. The Southwest Center website shares reusable content from both AWS and PAWS, including lecture notes, project descriptions, and audio and video of lectures. Through these thorough records, the efforts of the Southwest Center participants are made freely available to all. More information about the upcoming and past Arizona Winter School programs can be found at the Southwest Center's website: http://swc.math.arizona.edu/In 2022-2023, PAWS and AWS will be on "Unlikely Intersections." This topic concerns the expected finiteness of certain rare arithmetically or geometrically interesting intersections. For example, given a curve and a countable collection of "special" points in its ambient space, one expects the intersection of the curve with this set of points to be finite unless the curve is also "special." There has been substantial recent progress on the main conjectures and complementary problems of this field, especially on the André-Oort/Lang-Manin-Mumford/Zilber-Pink conjectures and analogues from arithmetic dynamics. This work draws together not just classical tools from algebraic and arithmetic geometry, but also tools from logic, heights, analytic number theory, dynamics, and p-adic geometry. The program will introduce students to the central problems, applications, and unique tools of this flourishing field.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.

在该奖项的支持下，西南算术几何中心将于 2023 年至 2025 年在亚利桑那州图森市的亚利桑那大学继续举办一系列年度“冬季学校”，首届将于 2023 年 3 月 4 日至 8 日举行。 1997年，西南中心的主要活动是亚利桑那州冬季学校（AWS），这一年会已成为一项重要的全国性活动，为学生提供高水平的培训和研究经验。 AWS 每年围绕不同的中心主题组织学生，并提供由领先和新兴专家精心设计和交付的一系列课程和相关研究项目，其结果是传统数学会议的独特融合。和研究研讨会：演讲者组织四到五场讲座的课程，并为研究生在会议期间提出研究项目，这些项目和单独的问题集由演讲者和博士后研究员主持。最后一天，学生向参与者展示他们的发现会议的结果是为所有参与者提供为期五天的特别紧张和集中的数学活动，西南中心将扩大其计划，以包括亚利桑那州初级冬季学校（PAWS）这一针对高年级本科生和初级研究生的虚拟计划。来自代表性不足群体的学生将在秋季学期围绕与 AWS 相同的主题举办两门为期六周的课程，参与者将参加由高级研究生举办的每周问题会议，并参加 AWS 的社区建设和指导活动。和 PAWS，对等点之间的连接是学生与高级研究人员之间的后续合作已成为常态，学生在成为研究数学家方面取得了具体进展，博士后助理在其学术生涯中获得了宝贵的指导经验，教师也开发了新的知识。西南中心网站分享来自 AWS 和 PAWS 的可重复使用的内容，包括讲座笔记、项目描述以及讲座的音频和视频。免费提供有关即将到来和过去的亚利桑那州冬季学校计划的更多信息，请访问西南中心的网站：http://swc.math.arizona.edu/2022-2023 年，PAWS 和 AWS 将在“不可能的交叉点”上进行。本主题涉及某些罕见的算术或几何上有趣的交点的预期有限性。例如，给定一条曲线和其周围空间中的“特殊”点的可数集合，人们期望具有这组点的曲线是有限的，除非该曲线也是“特殊的”。该领域的主要猜想和补充问题最近取得了实质性进展，特别是在 André-Oort/Lang-Manin-Mumford/Zilber 方面。 - 算术动力学中的粉红色猜想和类似物这项工作不仅汇集了代数和算术几何的经典工具，还汇集了逻辑、高度、解析数论、动力学和数学的工具。该项目将向学生介绍这个蓬勃发展领域的核心问题、应用和独特工具。该奖项是 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。