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：工具与应用”将于 2017 年 7 月 17 日至 21 日在伊利诺伊大学厄巴纳-香槟分校举行。该会议的主要目标是为最近的研究提供一个平台。同伦理论的发展，特别是它在中西部的发展。 这将通过多种方式来实现，主要是让精心挑选的 20 名国际专家组成的小组通过每周间隔一小时的全体会议分享前沿成果和发现。 还将在平行会议中安排一系列由志愿者主持的演讲，让年轻人、来自代表性不足群体的人以及来自小型机构的人向目标受众展示他们最近的工作。 此外，还将做出各种努力，创造有利于促进新的互动和发展未来合作的环境。 在过去的十年左右的时间里，同伦理论的学科范围得到了显着的扩大。 作为一门成熟的学科，同伦论的思想和方法已应用于不同领域（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、数学物理和表示理论（有时包含上述所有内容）。 此外，代数拓扑技术已被纳入分析大数据集的方法中，并在传感和医学领域得到应用。会议上的 20 场全体会议将由发言人发表，他们在开发抽象同伦理论、等变或彩色同伦理论工具方面的工作为上述同伦理论在其他领域的各种应用做出了贡献。 有关会议的更多信息，请访问 http://www.math.illinois.edu/homotopy2017/index.html