Homotopy Theory: Tools and 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