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 日在温哥华太平洋数学科学研究所 (PIMS) 举行的“算术拓扑”研讨会。近年来，数论的交叉领域取得了惊人的进展，特别是询问方程有多少个解的问题，以及研究形状和空间的数学性质的拓扑学。虽然数学家几十年来一直明白，各个方程都有一个相关的空间，其属性反映了方程，但许多自然方程（以及许多自然空间）都以无限序列出现。过去十年，我们在理解自然方程序列（“算术统计”）中的渐近行为如何控制方程组中的渐近行为以及受其控制方面取得了惊人的进步（部分导致了 Venkatesh 获得 2018 年菲尔兹奖，这是数学界的最高荣誉）。空间的自然序列（“同源稳定性”）。本次研讨会旨在汇集数论、代数几何和拓扑领域的不同领域的领先和新兴研究人员，以获得快速新兴的多学科领域的全球视野，培训参与者各种可用的方法，并产生强大的问题清单可以指导该领域未来 5-10 年的活动。过去十年里，代数拓扑、数论和代数几何的交叉领域爆发了一系列活动。这导致了丰富的：1）新定理，例如 Ellenberg-Venkatesh-Westerland 对函数域的 Cohen-Lenstra 启发式的证明； 2）拓扑学中启发式的新来源，例如 Vakil-Wood 对 Grothendieck 环的预测，或者 Farb-Wolfson-Wood 中的同调密度的概念和巧合； 3）使用现代拓扑工具对经典枚举定理进行改进，例如卡斯-维克尔格伦对立方体表面上27条线的算术计数； 4）重新关注不稳定的同源性，如 Galatius-Kupers-Randal-Williams 和 Miller-Wilson。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，将来自这些领域的不同初级和高级研究人员聚集在一起，目的是：1）让参与者对快速新兴的多学科领域有一个全球视野，2）让参与者详细了解可用方法的范围，以及3) 提出一个强有力的问题清单，可以帮助指导未来 5-10 年该领域的活动。更多信息可在会议上获得网站：https://www.pims.math.ca/scientific-event/190610-pwat。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。