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Noncommutative Geometry is a subfield of Functional Analysis with broad connections to several areas of mathematics. A foundational idea of the field, originating in quantum physics, is the notion that the quantization of a topological space is a noncommutative algebra. The theory of C*-algebras provides one way to make this precise. A celebrated theorem of Gelfand and Naimark implies that the category of commutative unital C*-algebras is equivalent to the category of compact Hausdorff topological spaces, while every noncommutative C*-algebra can be realized as an algebra of operators on Hilbert space. The research of members of this group focuses on diverse topics, such as the study of C*-algebras associated to dynamical systems, index theory of elliptic and hypoelliptic operators, groupoids, analytic and topological K-theory, Connes-Higson E-theory, and Fredholm manifolds.
