Marc Rieffel

{{short description|American mathematician}}

{{Infobox scientist

| birth_name = Marc Rieffel

| image = Rieffel.jpg

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| birth_date = {{birth date and age|1937|12|22}}

| birth_place = New York City, New York, United States

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| nationality = American

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| fields = C*-algebras
Quantum group theory
Noncommutative geometry

| workplaces = University of California, Berkeley

| alma_mater = Columbia University

| doctoral_advisor = Richard Kadison

| academic_advisors =

| doctoral_students = Philip Green
Jonathan Rosenberg

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| known_for = Noncommutative torus

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Marc Aristide Rieffel is a 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.[http://www.ams.org/profession/fellows-list 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 fractional linear transformations.{{cite journal|last=Rieffel|first=Marc A.|title=C*-Algebras Associated with Irrational Rotations|journal=Pacific Journal of Mathematics|year=1981|volume=93|issue=2|doi=10.2140/pjm.1981.93.415|pages=415–429 [416]|url=http://msp.org/pjm/1981/93-2/pjm-v93-n2-p12-s.pdf|access-date=28 February 2013|doi-access=free}} More recently, Rieffel has introduced a noncommutative analogue of Gromov-Hausdorff convergence for compact metric spaces which is motivated by applications to string theory.{{cite journal|last=Rieffel|first=Marc A.|title=Gromov-Hausdorff Distance for Quantum Metric Spaces/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance|journal=Memoirs of the American Mathematical Society|year=2004|doi=10.1090/memo/0796|s2cid=10059366|url=http://msp.org/pjm/1981/93-2/pjm-v93-n2-p12-s.pdf|access-date=17 December 2019}}

References