Marc Aristide Rieffel is an American mathematician noted for his fundamental contributions to C*-algebraG Cortinas (2008) K-theory and Noncommutative Geometry, European Mathematical Society. and quantum group theory.Symmetry, Integrability and Geometry: Methods and Applications (2014) vol 10; Special Issue on Noncommutative Geometry and Quantum Groups in honor of Marc A. Rieffel. He is currently a professor in the department of mathematics at the University of California, Berkeley.
In 2012, he was selected as one of the inaugural fellows of the American Mathematical Society.List of Fellows of the American Mathematical Society, retrieved 2014-03-17.
Contributions Rieffel earned his doctorate from Columbia University in 1963 under Richard Kadison with a dissertation entitled A Characterization of Commutative Group Algebras and Measure Algebras.
Rieffel introduced Morita equivalence as a fundamental notion in noncommutative geometry and as a tool for classifying C*-algebras. For example, in 1981 he showed that if Aθ denotes the noncommutative torus of angle θ, then Aθ and Aη are Morita equivalent if and only if θ and η lie in the same orbit of the action of SL(2, Z) on R by linear fractional transformations. More recently, Rieffel has introduced a noncommutative analogue of Gromov-Hausdorff convergence for compact metric spaces which is motivated by applications to string theory.
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