Marc Rieffel

Marc Aristide Rieffel is a mathematician noted for his fundamental contributions to C*-algebra[1] and quantum group theory.[2] He is currently a professor in the department of mathematics at the University of California, Berkeley.

Marc Rieffel
Born
Marc Rieffel

(1937-12-22) December 22, 1937
New York City, New York, United States
NationalityAmerican
Alma materColumbia University
Known forNoncommutative torus
Scientific career
FieldsC*-algebras
Quantum group theory
Noncommutative geometry
InstitutionsUniversity of California, Berkeley
Doctoral advisorRichard Kadison
Doctoral studentsPhilip Green
Jonathan Rosenberg

In 2012, he was selected as one of the inaugural fellows of the American Mathematical Society.[3]

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.[1] 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 fractional linear transformations.[4] More recently, Rieffel has introduced a noncommutative analogue of Gromov-Hausdorff convergence for compact metric spaces which is motivated by applications to string theory.[5]

References
  1. G Cortinas (2008) K-theory and Noncommutative Geometry, European Mathematical Society.
  2. Symmetry, Integrability and Geometry: Methods and Applications (2014) vol 10; Special Issue on Noncommutative Geometry and Quantum Groups in honor of Marc A. Rieffel.
  3. List of Fellows of the American Mathematical Society, retrieved 2014-03-17.
  4. Rieffel, Marc A. (1981). "C*-Algebras Associated with Irrational Rotations" (PDF). Pacific Journal of Mathematics. 93 (2): 415–429 [416]. doi:10.2140/pjm.1981.93.415. Retrieved 28 February 2013.
  5. Rieffel, Marc A. (2004). "Gromov-Hausdorff Distance for Quantum Metric Spaces/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance" (PDF). Memoirs of the American Mathematical Society. Retrieved 17 December 2019.
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