Summer School on Surgery and the Classification of Manifolds

外科和歧管分类暑期学校

• 批准号: 1638464
• 负责人: James Davis
• 金额: $ 2.14万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1638464&HistoricalAwards=false
• 关键词: Summer; Surgery; Classification; Manifolds

This award provides partial support towards the travel of US-based early-career mathematicians to the "Summer School on Surgery and the Classification of Manifolds" held at the University of Calgary, Alberta, Canada, on July 18-22, 2016. This international event is sponsored by the Pacific Institute of Mathematical Sciences (PIMS) Collaborative Research Group (CRG) in Applied, Algebraic, and Geometric Topology. Manifolds are geometric objects that locally resemble flat space. For example, the surface of a doughnut is a two-dimensional manifold called a torus. The technique of surgery, which involves cutting and pasting pieces of manifolds, allows a transition from questions in geometry to quantifiable and easier questions in algebra. The technique of surgery is a central area of mathematics, but it is quite difficult to learn because it draws on many other areas. This summer school is an educational outreach program designed to make the techniques of surgery and manifold topology accessible to a wide range of graduate students and junior mathematicians. The program includes lectures by experts, mini-lectures by participants on background topics, and exercise sessions mentored by experts. Graduate students, junior faculty, women, minorities, and persons with disabilities are especially encouraged to participate and to apply for support.Classification of manifolds is a central area of geometric topology and intersects with many other fields, including analysis, geometry, algebra, and group theory. This summer school aims to stimulate education and research in classification of manifolds and related areas of mathematics. Participants will have diverse mathematical backgrounds, with knowledge in geometric topology, algebraic topology, geometric group theory, differential geometry, and geometric functional analysis. Depending on interest, participants will have different take-aways from the summer school. A geometric topologist may learn about handle analysis and the specifics of the topology of manifolds. An algebraic topologist might learn about how classifying spaces, generalized (co)homology theories, and algebraic K-theory are used in practice. A geometer might learn about metrics of positive scalar curvature and tools for the topological classification of manifolds with geometric structure. A geometric group theorist might learn about applications of (co)homology of groups and large scale geometry. A geometric functional analyst would learn about a world parallel to that of C*-algebras and noncommutative geometry. The website of the summer school is http://www.pims.math.ca/scientific-event/160718-ssscm

该奖项为在2016年7月18日至22日在加拿大艾伯塔省卡尔加里大学在加拿大艾伯塔省卡尔加里大学举行的“暑期手术和歧管暑期学校的暑期学校和歧管分类”的旅行提供了部分支持。这项国际活动由Pacific Pacific Institute of Mathematical Sciences（PIMS）（PIMS）协作研究小组（PIMS）协作小组（CRGG）和GEERTRID ELPERID和Alge and Albraic，Alge and Algraic。歧管是局部类似于平坦空间的几何对象。例如，甜甜圈的表面是一种二维流形，称为圆环。手术技术涉及切割和粘贴歧管的碎片，可以从几何学中的问题转变为代数中的可量化和更轻松的问题。手术技术是数学的中心领域，但是很难学习，因为它在许多其他领域都借鉴。今年暑期学校是一项教育外展计划，旨在使众多研究生和初级数学家可以使用手术和多种拓扑技术。该计划包括专家的讲座，参与者关于背景主题的迷你讲座以及专家指导的练习课程。特别鼓励研究生，初级教师，妇女，少数民族和残疾人参与并申请支持。歧管的分类是几何拓扑结构的中心领域，并与许多其他领域相交，包括分析，几何学，代数，代数和小组理论。今年暑期学校旨在刺激数学流形和相关领域的分类的教育和研究。参与者将具有多种数学背景，并具有几何拓扑，代数拓扑，几何群体理论，差异几何和几何功能分析方面的知识。根据兴趣，参与者将与暑期学校不同。几何拓扑医生可能会学习有关手柄分析和歧管拓扑的细节。代数拓扑师可能会了解如何在实践中使用分类空间，广义（CO）同源理论和代数K理论。 地理表可以了解积极标态曲率的指标和具有几何结构的歧管拓扑分类的工具。几何群体理论家可能会了解（CO）组和大规模几何形状的应用。几何函数分析师将学习与C* - 代数和非共同几何形状平行的世界。暑期学校的网站是http://www.pims.math.ca/scientific-event/160718-SSSCM