Young Topologists Meeting 2015

2015年青年拓扑学家会议

• 批准号: 1509623
• 负责人: Joseph Hirsh
• 金额: $ 2.9万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-06-01 至 2017-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1509623&HistoricalAwards=false
• 关键词: Young; Topologists; Meeting; 2015

This travel grant provides partial support for U.S. participation in the international event "Young Topologists Meeting 2015," held at the Federal Polytechnical School in Lausanne, Switzerland, July 6-10, 2015. First started in 2007, the Young Topologists Meeting (YTM) is an annual European conference for graduate students and young researchers in in the field of topology. The subject of topology, the mathematical study of geometric properties that are independent of deformation, has importance throughout mathematics as well as in a large number of applications that range from theoretical physics to data analysis to robotic motion planning. The YTM offers junior topologists the opportunity to present their work to a large international audience, giving the speakers experience as well as facilitating the dissemination of research results. In addition, the YTM hosts two mini-courses by senior topologists that offer introductions to advanced topics and provide gateways into these subfields for even relatively inexperienced participants. This year the two mini-courses will stress both of the great successes of algebraic topology: theory-building and applications. One course will offer an introduction to the theory of Infinity Categories from a simple and formal perspective. Infinity categories are a relatively new framework for understanding many tools arising in mathematics and physics, including homological algebra, model categories, locality in field theories, and theories of A- and L-infinity algebras. Although infinity categories can be identified as playing a role in many areas of mathematics, their usefulness can be limited by their combinatorial intractability -- a problem which will be addressed by introducing infinity categories from this new viewpoint. The second course will address applications of algebraic topology to data science. In particular, it will describe the theory of Persistent Homology, which is a tool used to extract meaningful inference from both large and multi-dimensional data sets. As data becomes more ubiquitous, developing mathematical methods for handling large amounts of data is paramount, and this course will introduce the next generation of topologists to these problems and possible solutions through topology. The conference website can be found at http://gr-he.epfl.ch/ytm2015.

这笔旅行补助金为美国参加“2015 年青年拓扑学家会议”国际活动提供部分支持，该活动于 2015 年 7 月 6 日至 10 日在瑞士洛桑联邦理工学院举行。青年拓扑学家会议 (YTM) 于 2007 年首次启动是拓扑学领域研究生和年轻研究人员的年度欧洲会议。 拓扑学是对与变形无关的几何特性的数学研究，在整个数学以及从理论物理到数据分析再到机器人运动规划的大量应用中都具有重要意义。 YTM 为初级拓扑学家提供了向广大国际观众展示其工作的机会，为演讲者提供经验并促进研究成果的传播。此外，YTM 还举办了两门由高级拓扑学家主讲的迷你课程，介绍高级主题，并为相对缺乏经验的参与者提供进入这些子领域的门户。今年的两门迷你课程将强调代数拓扑的两大成功：理论构建和应用。一门课程将从简单而正式的角度介绍无穷范畴理论。无穷范畴是一个相对较新的框架，用于理解数学和物理学中出现的许多工具，包括同调代数、模型范畴、场论中的局部性以及 A 和 L 无穷代数理论。尽管无穷大范畴可以被认为在数学的许多领域中发挥着作用，但它们的有用性可能因其组合的棘手性而受到限制——这个问题将通过从这个新角度引入无穷大范畴来解决。第二门课程将讨论代数拓扑在数据科学中的应用。特别是，它将描述持久同源理论，这是一种用于从大型多维数据集中提取有意义的推理的工具。随着数据变得越来越普遍，开发处理大量数据的数学方法至关重要，本课程将向下一代拓扑学家介绍这些问题以及通过拓扑可能的解决方案。会议网站：http://gr-he.epfl.ch/ytm2015。