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.

该旅行赠款为美国参加国际活动“ 2015年年轻拓扑家会议”，在2015年7月6日至10日在瑞士洛桑联邦理工学院举行的国际活动提供了部分支持。年轻的拓扑师会议（YTM）是欧洲年轻的拓扑会议（YTM）。 拓扑的主题是独立于变形的几何特性的数学研究，在整个数学以及在从理论物理学到数据分析到机器人运动计划的大量应用中都具有重要的重要性。 YTM为初级拓扑师提供了机会，将其作品展示给大量的国际观众，从而为演讲者的经验以及促进了研究结果的传播。此外，YTM还主持了高级拓扑师的两个迷你演奏，他们向高级主题提供了介绍，并为这些子场提供了与相对缺乏经验的参与者的网关。今年，这两个迷你演奏将强调代数拓扑的巨大成功：理论建设和应用。一门课程将从简单而正式的角度从无限类别的理论进行介绍​​。无穷大类别是一个相对较新的框架，用于了解数学和物理学中产生的许多工具，包括同源代数，模型类别，现场理论中的局部性以及A-和L-内在代数的理论。尽管无穷大类别可以被确定为在许多数学领域中发挥作用，但它们的有用性可以受其组合棘手性的限制 - 这个问题将通过从这个新观点引入无限类别来解决。第二个课程将解决代数拓扑的应用到数据科学。特别是，它将描述持久性同源性的理论，该理论是一种用于从大型和多维数据集中提取有意义推断的工具。随着数据变得越来越普遍，开发用于处理大量数据的数学方法至关重要，本课程将通过拓扑引入下一代拓扑师和可能的解决方案。会议网站可以在http://gr-he.epfl.ch/ytm2015上找到。