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年一度的冬季学校系列活动，第一次将于2023年3月4日至8日举行。自1997年成立以来，西南中心的主要活动是亚利桑那州冬季学校(AWS)，这是一个年度会议，已成为全国知名活动，为研究生提供算术几何及相关领域的高水平培训和研究经验。AWS每年围绕一个不同的中心主题组织，由领先的和新兴的专家精心设计和提供一系列课程和配套的研究项目。其结果是传统数学会议和密集研究研讨会的独特融合：演讲者组织四到五个讲座的课程，并提出研究项目供研究生在会议期间开展工作。每晚关于这些项目和单独的问题集的工作会议由演讲者和博士后研究员主持。在最后一天，学生们向会议的参与者展示他们的发现。结果是，每个参与者都将进行为期五天的特别紧张和专注的数学活动。这一周期，西南中心将扩大其计划，包括初步亚利桑那州冬季学校(PAWS)。这一虚拟项目面向来自代表性不足群体的高级本科生和初级研究生，将在秋季学期推出两门为期六周的课程，围绕与AWS相同的主题组织。参与者将参加由高级研究生每周举办的问题课程，并参与社区建设和辅导活动。在AWS和PAWS，同行之间形成了联系，学生和高级研究人员之间建立了指导关系。各级参与者之间的后续协作是常态。学生们朝着成为研究数学家的方向迈出了具体的步伐，博士后助理在他们的学术生涯中获得了宝贵的指导经验，教师们培养了新的兴趣，看到了新的联系，导致了重要的出版成果。西南中心网站共享来自AWS和PAWS的可重复使用的内容，包括课堂讲稿、项目描述和讲座的音频和视频。通过这些透彻的记录，西南中心参与者的努力免费提供给所有人。关于即将和过去的亚利桑那州冬季学校项目的更多信息可以在西南中心的网站上找到：http://swc.math.arizona.edu/In 2022年-2023年，PAWS和AWS将在“不太可能的十字路口”。本主题涉及某些稀有的算术或几何上有意义的交集的预期有限性。例如，给定一条曲线及其周围空间中的一组“特殊”点，除非该曲线也是“特殊”的，否则人们会认为这条曲线与这组点的交集是有限的。在这一领域的主要猜想和互补问题上，特别是算术动力学中的André-Oort/Lang-Manin-Mumford/Zilber-Pink猜想和类似问题，最近已经取得了实质性的进展。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p进几何的工具。该计划将向学生介绍这个蓬勃发展的领域的核心问题、应用程序和独特的工具。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。