Workshop on Arithmetic and Topology Over Global Fields

该奖项将资助参加一个名为“全球领域的算术和拓扑”的研讨会，该研讨会将于2022年10月7日至9日在威斯康星大学麦迪逊分校举行。本次研讨会将集中讨论数学两个不同领域，数论和拓扑学之间的接口的发展。研讨会将汇集来自这两个学科的早期职业数学家，以便在这个已经活跃的领域之间的边界上推动进一步的进展。资金将集中在没有其他联邦资金的研究生、博士后和研究人员身上。我们的会议还将通过邀请许多备受瞩目的早期职业女性数学家来关注数学社区的包容性，并将申请与女性数学协会合作举办会议。有关研讨会最新信息的网页可在以下链接找到：https://sites.google.com/view/october-workshop/home。关于单性的问题在最近的研究中有很大的影响，如在品种的有理点和整点、特殊点、不可能交集、Selmer群的统计等领域。许多关于动机或代数循环的基本猜想也与单一性密切相关。本次会议的目的是汇集专家在各种拓扑方面的定义在算术基础上，给更广泛的听众包括研究生，博士后研究人员和其他数学家在算术几何工作。我们还希望研讨会成为各级参与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。我们希望在研讨会上由资深与会者所作的多样化的主题和演讲将为初级与会者提供一个了解该领域的新发展和问题的绝佳机会。我们为初级参与者，特别是研究生提供2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早期职业研究人员，他们将从这个快速发展的领域的介绍中获益最多。该奖项反映了美国国家科学基金会的法定使命，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。

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.