Homotopy Theory: Tools and Applications

同伦理论：工具和应用

• 批准号: 1719242
• 负责人: Vesna Stojanoska
• 金额: $ 4.5万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-07-01 至 2018-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1719242&HistoricalAwards=false
• 关键词: Homotopy; Theory; Tools; Applications

The week-long, international conference "Homotopy theory: Tools and Applications" will be held at the University of Illinois at Urbana-Champaign, July 17-21, 2017. The primary goal of the conference is to provide a platform for building on recent developments in homotopy theory, especially its growth in the Midwest. This will be accomplished in several ways, primarily by allowing a carefully selected group of 20 international experts to share cutting-edge results and discoveries via hour-long plenary talks spaced throughout the week. There will also be a series of talks scheduled in parallel sessions and presented by volunteers, allowing young people, those from underrepresented groups, and those from smaller institutions to present their recent work to this focused audience. In addition, various efforts will be made to create an environment conducive to fostering new interactions and the development of future collaborations.In the past decade or so, the subject of homotopy theory has seen a remarkable amplification of its scope. Already a mature subject, the ideas and methods of homotopy theory have been applied to diverse areas (sometimes under the guise of infinity-category theory), including algebraic and differential geometry, algebraic K-theory and motivic homotopy theory, mathematical physics, and representation theory (sometimes incorporating all of the above). In addition, the techniques of algebraic topology have been built into methods for analyzing large data sets, with applications in sensing and medicine. The 20 plenary talks at the conference will be given by speakers whose work in developing tools of abstract, equivariant, or chromatic homotopy theory has contributed to the aforementioned varied applications of homotopy theory in other areas. More information about the conference is available at http://www.math.illinois.edu/homotopy2017/index.html

为期一周的“同伦理论：工具与应用”国际会议将于2017年7月17日至21日在伊利诺伊大学香槟分校举行。会议的主要目标是提供一个平台，以发展同伦理论的最新发展，特别是它在中西部的发展。这将通过几种方式实现，主要是让精心挑选的20名国际专家通过整个星期长达一小时的全体会议分享尖端成果和发现。还将安排一系列由志愿者主持的平行讲座，让年轻人、来自代表性不足群体的年轻人和来自较小机构的年轻人向这些重点关注的听众介绍他们最近的工作。此外，还将努力创造有利于促进新的互动和未来合作发展的环境。在过去的十多年里，同伦理论的学科范围有了显著的扩大。同伦理论的思想和方法已经是一门成熟的学科，已经被应用到不同的领域(有时是以无穷范畴理论的名义)，包括代数和微分几何、代数K-理论和动机同伦理论、数学物理和表示理论(有时结合了以上所有内容)。此外，代数拓扑技术已成为分析大数据集的方法，并在传感和医学方面得到了应用。大会上的20场全体演讲将由演讲者进行，他们在开发抽象、等变或色同伦理论工具方面的工作有助于前述同伦理论在其他领域的各种应用。欲了解更多有关这次会议的信息，请访问http://www.math.illinois.edu/homotopy2017/index.html。