Research Training Group in Noncommutative Geometry

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Classic geometry such as algebraic geometry can be studied through commutative algebra. Noncommutative geometry is the study of the geometry and analysis of ``noncommutative spaces'' through operator algebras. Noncommutative geometry has important applications to many areas of mathematics including analysis, topology and geometry of manifolds, knot theory, mathematical physics. More recently, deep connections to number theory have been established. The breadth and technical nature of this subject has made it difficult for beginners to navigate to its frontiers. The noncommutative geometry group at Vanderbilt will establish a program of training PhD students and postdoctoral associates in the area of noncommutative geometry. In addition to the regular training program (such as courses and seminars), an important component of the program is the annual noncommutative geometry spring institute. The purpose of this school/conference is to train students and postdocs in noncommutative geometry and operator algebras. Several mini-courses will be given by leading experts and there will be additional research talks on recent progress in the subject. In addition the spring institute will provide a forum for young researchers to discuss their work with senior scientists.