Arizona Winter School in Arithmetic Geometry

亚利桑那大学举办“亚利桑那冬季学校”（AWS），这是一个为期一周的年度会议和研讨会，数学研究生和本科生在数论和算术几何研究前沿问题的领先专家的指导下学习和工作。该奖项支持AWS系列中的2020年、2021年和2022年会议。2020年亚利桑那州冬季学校将于3月9日至13日举行，主题为“非阿贝尔夏巴蒂”。"未来的主题将基于重要的数学发展和关键参与者的可用性。AWS通过促进新的研究和生成丰富的教学材料来推进数学，包括详细的课堂笔记、研究项目描述、问题会议大纲和所有讲座的高质量视频记录。这些来自过去AWS会议的资源，沿着有关即将到来的冬季学校主题和申请材料的信息，可通过AWS网站获得：www.example.com。AWS 2020将专注于Chabauty和科尔曼的方法，这是曲线算法的基石，也是关键的计算和理论工具。非阿贝尔技术随后给出了一个motivic证明有限的解决方案的单位方程，并奠定了基础的程序，推动p-adic分析技术超越了阿贝尔积分的限制。过去十年见证了快速的进步（和应用），尽管该主题的技术深度。为了有效地传播这样一个技术主题，系列讲座将密切协调，包括经典的Chabauty，计算方面和应用，高度，算术交叉理论，二次Chabauty，以及一系列关于概念和结构框架的讲座。AWS系列的潜在未来主题包括“志村变种”，这将使学生成为这个无处不在的理论的用户;“不太可能的交叉点”，这将调查几何有趣交叉点的有限性定理的最新进展（例如Manin-Mumford猜想和Andre-Oort猜想）;"算术几何算法的复杂性"，侧重于数论和代数几何算法的理论分析;和"超越GL_2的自守形式"，这将向学生介绍超越GL_2的群的自守形式，强调其应用于具体数字-该奖项反映了NSF的法定使命，并被认为是值得通过评估使用基金会的知识优点和更广泛的影响审查标准。

The University of Arizona hosts "Arizona Winter School" (AWS), an annual week-long conference and workshop in which mathematics graduate students and undergraduates learn from and work under the guidance of leading experts on questions at the forefront of research in number theory and arithmetic geometry. This award supports the 2020, 2021, and 2022 meetings in the AWS series. The 2020 Arizona Winter School will be held from March 9-13 on the topic of "Non-Abelian Chabauty." Future topics will be based on important mathematical developments and the availability of key participants. AWS advances mathematics by catalyzing new research and generating a wealth of pedagogical materials, including detailed lecture notes, research project descriptions, problem session outlines, and high-quality video recordings of all the lectures. These resources from past AWS conferences, along with information about upcoming Winter School topics and application materials, are available through the AWS website: http://swc.math.arizona.edu/. AWS 2020 will focus on the method of Chabauty and Coleman, a cornerstone of the arithmetic of curves and a key computational and theoretical tool. Non-abelian techniques subsequently gave a motivic proof of finiteness of solutions to the unit equation and laid the foundations of a program to push p-adic analytic techniques beyond the limitations of abelian integrals. The last decade has witnessed rapid progress (and applications), despite the technical depth of the subject. To effectively disseminate such a technical topic, the lecture series will be closely coordinated, and include classical Chabauty, computational aspects and applications, heights, arithmetic intersection theory, quadratic Chabauty, and a series of lectures about the conceptual and conjectural framework. Potential future topics for the AWS series include "Shimura Varieties," which would prepare students to be users of this ubiquitous theory; "Unlikely Intersections," which would survey recent advances on finiteness theorems for geometrically interesting intersections (e.g. the conjectures of Manin-Mumford and the Andre-Oort conjecture); "Complexity of Arithmetic Geometry Algorithms," which would focus on the theoretical analysis of algorithms in number theory and algebraic geometry; and "Automorphic Forms Beyond GL_2," which would introduce students to automorphic forms on groups beyond GL_2, emphasizing their applications to concrete number-theoretic 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.