Summer School on Surgery and the Classification of Manifolds

该奖项为美国早期数学家参加2016年7月18日至22日在加拿大阿尔伯塔省卡尔加里大学举行的“外科手术和流形分类暑期班”提供了部分支持。这一国际活动由太平洋数学科学研究所(PIMS)应用、代数和几何拓扑学合作研究小组(CRG)赞助。流形是局部类似于平面空间的几何对象。例如，甜甜圈的表面是一个称为环面的二维流形。外科手术的技术包括切割和粘贴流形的片断，允许从几何问题过渡到代数中可量化的更容易的问题。外科手术技术是数学的中心领域，但它很难学习，因为它涉及到许多其他领域。这个暑期班是一个教育推广项目，旨在让广大研究生和初级数学家能够接触到外科技术和多种拓扑学。该项目包括专家讲座，参与者关于背景主题的迷你讲座，以及专家指导的锻炼课程。特别鼓励研究生、初级教师、女性、少数族裔和残疾人参与并申请支持。流形分类是几何拓扑学的核心领域，与许多其他领域交叉，包括分析、几何、代数和群论。这个暑期班旨在促进流形分类和相关数学领域的教育和研究。学员将具有不同的数学背景，掌握几何拓扑学、代数拓扑学、几何群论、微分几何和几何泛函分析等知识。根据兴趣的不同，参与者将从暑期班获得不同的收获。几何拓扑学家可以学习句柄分析和流形拓扑的细节。代数拓扑学家可以学习如何在实践中使用分类空间、广义(余)同调理论和代数K-理论。几何学家可以学习正标量曲率的度量和具有几何结构的流形的拓扑分类工具。几何群论家可以学习群的(余)同调和大规模几何的应用。几何泛函分析员将了解一个与C*-代数和非对易几何平行的世界。暑期班的网站是http://www.pims.math.ca/scientific-event/160718-ssscm

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