Homotopical Group Theory and Topological Algebraic Geometry, June 2008

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This project will support travel to the conference "Homotopical Group Theory and Topological Algebraic Geometry,"at the University of Copenhagen and at the Max Planck Institut in Bonn in June 2008. Homotopical Group Theory and Topological Algebraic Geometry involve the interaction at the highest level of formerly distant areas of mathematics. They are bound together by a common toolbox from modern homotopy theory. Homotopical Group Theory has shed light on fundamental issues such as the structure of classifying spaces and group actions, and the nature and classification of compact Lie groups. It has very recently shown the potential of shedding new light on the classification of finite simple groups. Topological Algebraic Geometry brings together ideas from algebraic geometry and homotopy theory. It has contributed to significant advances in bothareas, including elliptic cohomology and the relationship between the chromatic stable homotopy theory and the Langlands program.Homotopical Group Theory and Topological Algebraic Geometry are new areas of mathematics, and they have recently enjoyed explosive development by researchers around the world. The conference supported by this proposal will begin at the University of Copenhagen, focused on two series of lectures by Paul Goerss of Northwestern University and Bill Dwyer of the University of Notre Dame and aimed at beginning researchers. The following week at the Max Planck Institut, leading researchers will report on the latest developments. The idea is to bring together current leaders and new researchers, and to enable interaction and cross-fertilization of ideas among a broad group of mathematicians.