Young Topologists Meeting 2015

这笔旅行补助金为美国参加2015年7月6日至10日在瑞士洛桑的联邦理工学院举行的国际活动“2015年青年拓扑学家会议”提供部分支持。 青年拓扑学家会议（Young Topologists Meeting，简称YTM）始于2007年，是欧洲拓扑学领域研究生和年轻研究人员的年度会议。 拓扑学的主题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到机器人运动规划的大量应用中具有重要性。 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，为演讲者提供了经验，并促进了研究成果的传播。此外，YTM还举办了两个由高级拓扑学家举办的小型课程，为高级主题提供介绍，并为相对缺乏经验的参与者提供进入这些子领域的门户。今年的两个迷你课程将强调代数拓扑学的巨大成功：理论建设和应用。其中一门课程将从一个简单而正式的角度介绍无限范畴理论。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-无穷代数的理论。虽然无穷大范畴可以被确定为在数学的许多领域发挥作用，它们的有用性可能受到其组合的棘手性的限制-一个问题，这将通过引入无穷大范畴从这个新的观点来解决。第二门课程将讨论代数拓扑在数据科学中的应用。特别是，它将描述持久同源性理论，这是一种用于从大型和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是至关重要的，本课程将介绍下一代拓扑学家通过拓扑学解决这些问题和可能的解决方案。会议的网址是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.