Young Topologists Meeting 2015

这笔旅行补助金为美国参加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“2015年青年拓扑学家会议”提供了部分支持。青年拓扑学家会议(YTM)始于2007年，是一年一度的欧洲拓扑学领域研究生和青年研究人员会议。拓扑学是对与变形无关的几何性质的数学研究，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大量国际观众展示他们的工作的机会，给演讲者带来了体验，并促进了研究成果的传播。此外，YTM举办了两个由资深拓扑学家举办的小型课程，提供高级主题的介绍，并为即使是相对缺乏经验的参与者提供进入这些子领域的途径。今年的两门迷你课程将强调代数拓扑学的两大成就：理论构建和应用。其中一门课程将从简单和正式的角度介绍无穷大范畴的理论。无穷大范畴是一个相对较新的框架，用于理解数学和物理中出现的许多工具，包括同调代数、模型范畴、场论中的局部性以及A-和L-无限代数理论。虽然无穷大范畴可以被认为在数学的许多领域中发挥作用，但它们的有用性可能受到它们的组合难解性的限制--这个问题将通过从这个新的观点引入无限大范畴来解决。第二门课程将介绍代数拓扑学在数据科学中的应用。特别是，它将描述持久同调理论，这是一种用于从大型和多维数据集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是至关重要的，本课程将向下一代拓扑学家介绍这些问题和通过拓扑学可能的解决方案。会议网址为：http://gr-he.epfl.ch/ytm2015.。

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.