Homotopy Theory: Tools and Applications

为期一周的国际会议“同伦理论：工具与应用”将于2017年7月17-21日在伊利诺伊大学厄巴纳-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。这将通过几种方式实现，主要是允许精心挑选的20名国际专家小组通过一周内间隔的一小时全体会议来分享前沿成果和发现。还将在平行会议上安排一系列由志愿者主持的讲座，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听众介绍他们最近的工作。此外，将作出各种努力，创造有利于促进新的相互作用和发展未来合作的环境。在过去十年左右的时间里，同伦理论的研究范围有了显著的扩大。作为一个成熟的学科，同伦理论的思想和方法已经被应用到不同的领域（有时在无限范畴理论的幌子下），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（有时结合上述所有）。此外，代数拓扑技术已被构建到分析大型数据集的方法中，并在传感和医学中得到应用。会议的20个全体会议将由在发展抽象、等变或色同伦理论工具方面的工作对上述同伦理论在其他领域的各种应用作出贡献的演讲者进行。有关会议的更多信息，请访问http://www.math.illinois.edu/homotopy2017/index.html

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