Arithmetic Topology Conference

算术拓扑会议

基本信息

批准号：
1856737
负责人：
Jesse Wolfson
金额：
$ 2.7万
依托单位：
University of California-Irvine
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-06-01 至 2020-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1856737&HistoricalAwards=false
关键词：
Arithmetic Topology Conference

项目摘要

This award supports US participants to attend the workshop "Arithmetic Topology" at the Pacific Institute of Mathematical Sciences (PIMS) from June 10-14, 2019 in Vancouver. Recent years have seen spectacular advances at the intersection of number theory, specifically problems asking how many solutions an equations has, and topology which studies mathematical properties of shapes and spaces. While mathematicians have understood for several decades that individual equations have an associated space whose properties reflect the equation, many natural equations (and many natural spaces) come in infinite sequences. The last decade has seen spectacular advances (leading in part to Venkatesh's 2018 Fields Medal, highest honor in mathematics) in our understanding of how the asymptotic behavior in natural sequences of equations ("arithmetic statistics") governs and is governed by the asymptotic behavior in natural sequences of spaces ("homological stability"). This workshop aims to bring together a diverse group of leading and emerging researchers working in number theory, algebraic geometry and topology to obtain a global view of a fast emerging and multidisciplinary area, to train participants in the range of methods available, and to generate a robust problem list that can guide activity in the area for the next 5-10 years. The last 10 years have brought a burst of activity at the intersection of algebraic topology, number theory and algebraic geometry. This has led to a wealth of:1) new theorems, such as Ellenberg-Venkatesh-Westerland's proof of theCohen-Lenstra heuristics for function fields; 2) new sources of heuristics in topology, such as Vakil-Wood's predictions from the Grothendieck ring, or the notion and coincidences of homological densities as in Farb-Wolfson-Wood; 3) refinements of classical enumerative theorems using modern topological tools, such as Kass-Wickelgren's arithmetic count of the 27 lines on a cubic surface; and4) a renewed focus on unstable homology, as in Galatius-Kupers-Randal-Williams and Miller-Wilson. The organizers of the workshop believe that these results are just the beginning of the emerging area of arithmetic topology. They are organizing a 5 day workshop to bring together a diverse group of junior and senior researchers from across these areas with the goal of: 1) giving participants a global view of a fast emerging and multidisciplinary area,2) giving participants a detailed awareness on the range of methods available, and3) emerging with a robust problem list which can help guide activity in the area for the next 5-10 years.More information is available at the conference website:https://www.pims.math.ca/scientific-event/190610-pwat.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.

该奖项支持美国参与者参加2019年6月10日至14日在温哥华的太平洋科学研究所（PIMS）参加研讨会的“算术拓扑”。近年来，在数字理论的交集中看到了壮观的进步，特别是询问方程有多少解决方案的问题，以及研究形状和空间的数学特性的拓扑。数学家已经了解了几十年，即单个方程具有相关的空间，其特性反映了方程，但许多天然方程（和许多自然空间）都以无限的序列出现。在过去的十年中，在我们理解方程式（“算术统计量”）中如何支配了渐近行为（“算术统计”）如何控制并受到空间自然序列中的渐近行为的控制（“同源稳定性”（“同源稳定性”），过去十年中的壮观进步（部分导致了Venkatesh的2018年奖章，数学中最高荣誉，数学中的最高荣誉）。该研讨会旨在汇集一组领先的和新兴的研究人员，从事数字理论，代数几何和拓扑工作，以获取对快速新兴和多学科领域的全球视图，以培训参与者可用的方法，并在未来5 - 10年的时间内引起一个可靠的问题列表，以引起强大的问题列表。在过去的10年中，在代数拓扑，数理论和代数几何形状的交集中带来了一系列活动。这导致了很多：1）新定理，例如Ellenberg-Venkatesh-Westerland证明功能领域的Thecohen-Lenstra启发式方法； 2）拓扑启发式方法的新来源，例如Vakil-Wood从Grothendieck戒指中的预测，或Farb-Wolfson-Wood中的同源密度的概念和巧合； 3）使用现代拓扑工具（例如Kass-Wickelgren在立方表面上的27行的算术计数）对经典枚举定理进行了改进；和4）重点是不稳定同源性的，就像在加拉图斯·库普斯 - 兰德·韦利亚姆（Galatius-Bupers-Williams）和米勒·威尔森（Miller-Wilson）一样。研讨会的组织者认为，这些结果只是算术拓扑新兴领域的开始。他们正在组织一个为期5天的研讨会，将来自这些领域的各种各样的初级和高级研究人员组合在一起，目的是：1）让参与者对快速新兴和多学科领域的全球视野，2）2）为参与者提供详细的认识，使参与者对可用方法的范围详细了解，以及3）在该领域的强大问题中，可以在下一个5-10年的活动中进行指导。网站：https：//www.pims.math.ca/scientific-event/190610-pwat.this Trawe反映了NSF的法定任务，并被认为是值得通过基金会的知识分子的评估来获得支持的，并具有更广泛的影响。