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

为期一周的国际会议“同伦理论：工具和应用”将于2017年7月17日至21日在伊利诺伊大学香槟分校举行。 会议的主要目标是为同伦理论的最新发展提供一个平台，特别是它在中西部的发展。 这将通过几种方式来实现，主要是让一个精心挑选的20名国际专家小组通过为期一周的长达一小时的全体会议分享尖端成果和发现。 还将在平行会议中安排一系列讲座，由志愿者主讲，让年轻人、代表性不足的群体和较小机构的人向重点听众介绍他们最近的工作。 此外，还将通过各种努力，创造有利于促进新的相互作用和未来合作发展的环境。在过去的十多年中，同伦理论的范围得到了显着的扩大。 同伦理论已经是一门成熟的学科，其思想和方法已应用于不同的领域（有时以无穷范畴理论为幌子），包括代数和微分几何、代数K理论和动机同伦理论、数学物理和表示论（有时包含上述所有内容）。 此外，代数拓扑学的技术已经被构建成用于分析大型数据集的方法，并在传感和医学中得到应用。在会议上的20个全体会议将由发言者，他们的工作在开发工具的抽象，等变，或色同伦理论作出了贡献，上述各种应用同伦理论在其他领域。 有关会议的更多信息，请访问http://www.math.illinois.edu/homotopy2017/index.html