Workshop on Arithmetic and Topology Over Global Fields

该奖项将资助参加将于2022年10月7日至9日在威斯康星大学麦迪逊分校举行的题为“全球领域的算术和拓扑学”的研讨会。这个工作坊将集中在数论和拓扑学这两个不同数学领域之间的界面上的发展。研讨会将把这两个学科的早期数学家聚集在一起，以推动在这一领域之间本已活跃的边界上取得进一步进展。资金将集中在研究生、博士后和研究人员身上，没有其他联邦资金。我们的会议还通过邀请许多高调的职业生涯早期女性数学家来关注数学界的包容性，并将申请与妇女数学协会合作设立会议。有关工作坊的最新资料，请浏览以下网页：https://sites.google.com/view/october-workshop/home.与单列有关的问题在最近的工作中影响很大，如关于簇的有理点和积分点、特殊点、不可能交、Selmer群的统计等。许多关于动机或代数循环的基本猜想也与单列密切相关。本次会议旨在将算术基上定义的变种的各种拓扑方面的专家聚集在一起，向更广泛的听众发表演讲，这些听众包括研究生、博士后研究人员和其他从事算术几何工作的数学家。我们的目标还是使研讨会成为各级与会者见面和面对面交谈的环境，并寻求新的合作，在整个领域产生影响。我们希望，高级学员在讲习班上所作的各种专题和演讲将为初级学员提供一个极好的机会，让他们了解这一领域的新发展和新问题。我们为初级参与者，特别是研究生，提供了两个小时的海报会议，向专家和同行展示他们的项目和成果。我们的广告和招聘将优先考虑研究生和职业生涯早期的研究人员，他们将从这一快速发展的领域的介绍中受益最大。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。

The award will fund participation in a workshop titled "Arithmetic and topology over global fields," to be held October 7-9, 2022 at the University of Wisconsin-Madison. This workshop will focus on developments at the interface between two different fields of math, number theory and topology. The workshop will bring together early-career mathematicians from both subjects in order to spur further progress at this already-active boundary between fields. Funding will be concentrated on graduate students, postdocs, and researchers without other federal funding. Our conference also focuses on inclusiveness in the math community by inviting many high-profile early-career female mathematicians, and will apply to set up the conference in cooperation with the Association for Women in Mathematics. A webpage with up-to-date information about the workshop can be found at this link: https://sites.google.com/view/october-workshop/home. Questions pertaining to monodromy have been highly influential on recent work in areas like rational and integral points on varieties, special points, unlikely intersections, statistics of Selmer groups, etc. Many fundamental conjectures about motives or algebraic cycles are also deeply connected to monodromy. This conference aims to bring together experts on various topological aspects of varieties defined over arithmetic bases to give talks to a wider audience consisting of graduate students, postdoctoral researchers and other mathematicians working in arithmetic geometry. We also aim for the workshop to be an environment for the participants at all levels to meet and talk in person, and seek new collaborations, creating impact throughout the field. We hope that the diversity of topics and talks given by senior participants in the workshop will provide a fantastic opportunity for the junior participants to learn about new developments and questions in the field. We provide a 2-hour poster session for the junior participants, especially graduate students, to present their projects and results to experts and peers. Our advertisement and recruitment will prioritize graduate students and early-career researchers, who stand to benefit the most from an introduction to this quickly-moving area.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.