Marc Rieffel
{{short description|American mathematician}}
{{Infobox scientist
| birth_name = Marc Rieffel
| image = Rieffel.jpg
| image_size =
| birth_date = {{birth date and age|1937|12|22}}
| birth_place = New York City, New York, United States
| death_date =
| death_place =
| citizenship =
| nationality = American
| ethnicity =
| 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
| notable_students =
| known_for = Noncommutative torus
| author_abbrev_zoo =
| influences =
| influenced =
| awards =
| religion =
| signature =
| footnotes =
}}
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
External links
- {{MathGenealogy|id=30549}}
{{Authority control}}
{{DEFAULTSORT:Rieffel, Marc}}
Category:20th-century American mathematicians
Category:21st-century American mathematicians
Category:Columbia Graduate School of Arts and Sciences alumni
Category:Fellows of the American Mathematical Society