Jonathan Rosenberg (mathematician)

Jonathan Rosenberg, Oberwolfach 2005

Jonathan Micah Rosenberg (born December 30, 1951 in Chicago , Illinois ) is an American mathematician who deals with algebraic topology , operator algebras , K-theory and representation theory , with mathematical applications in string theory (dualities).

Rosenberg received his doctorate in 1976 with Marc Rieffel at the University of California, Berkeley ( Group C * -algebras and square integrable representations ). From 1977 to 1981 he was an assistant professor at the University of Pennsylvania and since 1981 he has been an associate professor at the University of Maryland in College Park , and from 1985 as a professor. There he is Ruth M. Davis Professor of Mathematics.

He deals with operator algebras and their relationships to topology, geometry, the unitary representation theory of Lie groups, K-theory and index theory.

The Gromov-Lawson-Rosenberg conjecture is named after him, H. Blaine Lawson and Michail Leonidowitsch Gromow . The conjecture gives a criterion for the existence of a metric with positive scalar curvature on smooth, connected compact manifolds without a boundary in five or more dimensions. Gromov and Lawson showed the invariance of the question of the existence of such a metric under surgery if the dimension is high enough and with a simple connection. Rosenberg treated the case of nontrivial fundamental groups and used K-theory invariants to formulate an obstruction criterion for the existence of such a metric.

Rosenberg showed close connections between the Gromov-Lawson conjecture and the Novikov conjecture (a central open problem in algebraic topology) and, together with Stephan Stolz, formulated a “stable” form of the conjecture that they were able to prove for a number of fundamental groups.

Since 2007 he has been editor of the Journal of K-Theory. From 2000 to 2003 he was Associate Editor of the Journal of the American Mathematical Society and from 1988 to 1992 of Proceedings of the AMS. From 1981 to 1984 he was a Sloan Research Fellow . He is a fellow of the American Mathematical Society .

He has been married to Jeanne Sauber since 1990 and has two children.

Fonts

with Elliot C. Gootman: The structure of crossed product -algebras: a proof of the generalized Effros-Hahn conjecture. ${\ displaystyle C ^ {*}}$ In: Inventiones Mathematicae . Vol. 52, No. 3, 1979, pp. 283-298 .
${\ displaystyle C ^ {*}}$ -algebras, positive scalar curvature, and the Novikov Conjecture.
- Part 1 in: Institut des Hautes Etudes Scientifiques. Publications Mathématiques. Volume 58, 1983, pp. 197-212, ( online );
- Part 2 in: Huzihiro Araki , Eduard G. Effros (Ed.): Geometric Methods in Operator Algebras. Proceedings of the US-Japan Joint Seminar on Geometric Methods in Operator Algebras, Kyoto, July 1983 (= Pitman Research Notes in Mathematics Series. 123). Longman, Harlow (Essex) 1986, ISBN 0-582-99456-X , pp. 341-374
- Part 3 in: Topology. Vol. 25, No. 3, 1986, pp. 319-336, doi : 10.1016 / 0040-9383 (86) 90047-9 .
with Claude Schochet: The Künneth theorem and the universal coefficient theorem for equivariant K-theory and KK-theory (= Memoirs of the American Mathematical Society. 348). American Mathematical Society, Providence RI 1986, ISBN 0-8218-2349-3 .
with Claude Schochet: The Künneth theorem and the universal coefficient theorem for Kasparov's generalized -functor. ${\ displaystyle K}$ In: Duke Mathematical Journal . Vol. 55, No. 2, 1987, pp. 431-474, doi : 10.1215 / S0012-7094-87-05524-4 .
The assembly map and positive scalar curvature. ${\ displaystyle KO}$ In: Stefan Jackowski, Bob Oliver, Krzystof Pawałowski (eds.): Algebraic Topology Poznań 1989. Proceedings of a conference held in Poznań, Poland, June 22-27, 1989 (= Lecture Notes in Mathematics . 1474). Springer, Berlin et al. 1991, ISBN 3-540-54098-9 , pp. 170-182.
with Stephan Stolz: A "stable" version of the Gromov-Lawson conjecture. In: Mila Cenkl, Haynes Miller (eds.) The Čech centennial. A Conference on Homotopy Theory, June 22-26 1993, Northeastern University (= Contemporary Mathematics . 181). American Mathematical Society, Providence RI 1995, ISBN 0-8218-0296-8 , pp. 405-418.
as editor with Steven C. Ferry, Andrew Ranicki : Novikov Conjectures, Index Theorems and Rigidity. Oberwolfach 1993 (= London Mathematical Society. Lecture Notes Series. 226-227). 2 volumes. Cambridge University Press, Cambridge et al. 1995, ISBN 0-521-49796-5 (Vol. 1), ISBN 0-521-49795-7 (Vol. 2);
- in Volume 1, pp. 7-66: Ferry, Ranicki, Rosenberg: History and Survey of the Novikov Conjecture.
- in Volume 1, pp. 338-372: Rosenberg: Analytic Novikov for Topologists.
Algebraic K-Theory and its Applications (= Graduate Texts in Mathematics . 147). Springer, New York NY et al. 1996, ISBN 3-540-94248-3 .
with Kevin R. Coombes, Ronald L. Lipsman: Multivariable calculus and Mathematica. With applications to geometry and physics , Springer, New York NY et al. 1998, ISBN 0-387-98360-0 .
as editor with Sylvain Cappell , Andrew Ranicki: Surveys on Surgery Theory. Papers dedicated to CTC Wall (= Annals of Mathematics Studies. 145 and 149). 2 volumes. Princeton University Press, Princeton NJ et al. 2000-2001, ISBN 0-691-04937-8 (Vol. 1), ISBN 0-691-08814-4 (Vol. 2);
- in Volume 2, pp. 353-389: Rosenberg, Stephan Stolz: Metrics of positive scalar curvature and connections with surgery.
with Joachim Cuntz , Ralf Meyer: Topological and bivariant K-theory (= Oberwolfach Seminars. 36). Birkhäuser Basel et al. 2007, ISBN 978-3-7643-8398-5 .
as editor with Robert S. Doran, Greg Friedman: Superstrings, geometry, topology, and -algebras. (NSF-CBMS Regional Conference on Mathematics on Topology, -Algebras, and String Duality, held at Texas Christian University, Fort Worth, Texas, May 18-22, 2009) ${\ displaystyle C ^ {*}}$ ${\ displaystyle C *}$ (= Proceedings of Symposia in Pure Mathematics. 81). American Mathematical Society, Providence RI 2010, ISBN 978-0-8218-4887-6 .

Web links

Individual evidence

↑ Life data according to American Men and Women of Science , Thomson Gale 2004
^ Mathematics Genealogy Project
↑ Gromov, Lawson: The classification of simply connected manifolds of positive scalar curvature. In: Annals of Mathematics . Series 2, Vol. 111, No. 3, 1980, pp. 423-434, doi : 10.2307 / 1971103 ; Gromov, Lawson: Positive scalar curvature and the Dirac Operator on complete Riemannian Manifolds. In: Institut des Hautes Etudes Scientifiques. Publications Mathématiques. Volume 58, 1983, pp. 83-196, ( online ); tightened by Rosenberg: The -assembly map and positive scalar curvature. ${\ displaystyle KO}$ In: Jackowski, Oliver, Pawałowski (eds.): Algebraic Topology Poznań 1989. 1991, pp. 170–182.
^ Gilkey Gromov Lawson conjecture , Encyclopedia of Mathematics, Springer Verlag

personal data
SURNAME	Rosenberg, Jonathan
ALTERNATIVE NAMES	Rosenberg, Jonathan Micah (full name)
BRIEF DESCRIPTION	American mathematician
DATE OF BIRTH	December 30, 1951
PLACE OF BIRTH	Chicago , Illinois

[1] Life data according to American Men and Women of Science , Thomson Gale 2004

[2] Mathematics Genealogy Project

[3] Gromov, Lawson: The classification of simply connected manifolds of positive scalar curvature. In: Annals of Mathematics . Series 2, Vol. 111, No. 3, 1980, pp. 423-434, doi : 10.2307 / 1971103 ; Gromov, Lawson: Positive scalar curvature and the Dirac Operator on complete Riemannian Manifolds. In: Institut des Hautes Etudes Scientifiques. Publications Mathématiques. Volume 58, 1983, pp. 83-196, ( online ); tightened by Rosenberg: The -assembly map and positive scalar curvature. ${\ displaystyle KO}$ In: Jackowski, Oliver, Pawałowski (eds.): Algebraic Topology Poznań 1989. 1991, pp. 170–182.

[4] Gilkey Gromov Lawson conjecture , Encyclopedia of Mathematics, Springer Verlag