Jonathan M. Rosenberg

Primary research areas:

Representation theory of Lie groups, C*-algebras, K-theory, topology and geometry of manifolds, index theory of elliptic operators, related areas of mathematical physics.

Some old publications now available on the web:
  1. Comments on a paper of I. D. Brown and Y. Guivarc'h, Annales Scientifiques de l'École Normale Supérieure (4) 8 (1975), 379-381. (For the Brown-Guivarc'h paper itself, see here.)
  2. The C*-algebras of some real and p-adic solvable groups, Pacific J. Math. 65 (1976), no. 1, 175-192.
  3. Frobenius reciprocity for square-integrable factor representations, Illinois Journal of Mathematics 21 (1977), no. 4, 818-825.
  4. A Quick Proof of Harish-Chandra's Plancherel Theorem for Spherical Functions on a Semisimple Lie Group, Proc. Amer. Math. Soc. 63 (1977), 143-149.
  5. Remarks on random walks on semi simple Lie groups, Mémoires de la Société Mathématique de France 54 (1977), 119-127.
  6. Amenability of crossed products of C*-algebras, Comm. Math. Phys. 57 (1977), no. 2, 187-191.
  7. (with Edward Effros) C*-algebras with approximately inner flip, Pacific J. Math. 77 (1978), no. 2, 417--443.
  8. Square-Integrable Factor Representations of Locally Compact Groups, Trans. Amer. Math. Soc. 237 (1978), 1-33.
  9. Appendix to "Crossed products of UHF algebras by product type actions" by Ola Bratteli, Duke Math. J. 46 (1979), no. 1, 25--26.
  10. (with E. Gootman) The structure of crossed product C*-algebras: a proof of the generalized Effros-Hahn conjecture, Invent. Math. 52 (1979), no. 3, 283--298.
  11. Realization of Square-Integrable Representations of Unimodular Lie Groups on L2-Cohomology Spaces, Trans. Amer. Math. Soc. 261 (1980), 1-32.
  12. (with Claude Schochet) The classification of extensions of C*-algebras, Bull. Amer. Math. Soc. (N.S.) 4 (1981), no. 1, 105-110.
  13. (with Claude Schochet) Comparing functors classifying extensions of C*-algebras, J. Operator Theory 5 (1981), no. 2, 267-282.
  14. (with Richard Herman) Norm-close group actions on C*-algebras, J. Operator Theory 6 (1981), no. 1, 25-37.
  15. The role of K-theory in noncommutative algebraic topology, in Operator algebras and K-theory (San Francisco, Calif., 1981), pp. 155-182, Contemp. Math., 10, Amer. Math. Soc., Providence, R.I., 1982.
  16. C*-algebras, positive scalar curvature, and the Novikov conjecture, Publ. Math. IHES 58 (1983), 197-212.
  17. C*-algebras, positive scalar curvature and the Novikov conjecture. II in Geometric methods in operator algebras (Kyoto, 1983), 341--374, Pitman Res. Notes Math. Ser., 123, Longman Sci. Tech., Harlow, 1986.
  18. Group C*-algebras and topological invariants, Operator algebras and group representations, Vol. II (Neptun, 1980), 95-115, Monogr. Stud. Math., 18, Pitman, Boston, MA, 1984.
  19. Some results on cohomology with Borel cochains, with applications to group actions on operator algebras, Operator Theory: Advances and Applications, vol. 17, Birkhäuser, 1986, pp. 301-330.
  20. (with Steven Hurder, Dorte Olesen, and Iain Raeburn) The Connes spectrum for actions of abelian groups on continuous-trace algebras, Ergodic Thy. and Dyn. Systems 6 (1986), no. 4, 541-560.
  21. C*-algebras, positive scalar curvature, and the Novikov conjecture, III, Topology 25, no. 3 (1986), 319-336.
  22. (with Claude Schochet) The Künneth theorem and the universal coefficient theorem for Kasparov's generalized K-functor, Duke Math. J. 55, no. 2 (1987), 431-474.
  23. Quasidiagonality and nuclearity (appendix to a paper of D. Hadwin), J. Operator Theory 18 (1987), 15-18.
  24. Applications of analysis on Lipschitz manifolds, Miniconferences on harmonic analysis and operator algebras, Proc. Centre for Mathematical Analysis, Austral. Nat. Univ., vol. 16, 1988.
  25. (with Iain Raeburn) Crossed Products of Continuous-Trace C*-Algebras by Smooth Actions, Trans. Amer. Math. Soc. 305 (1988), 1-45.
  26. Continuous-Trace -Algebras from the Bundle Theoretic Point of View, J. Australian Math. Soc. (Ser. A) 47 (1989), 368-381.
  27. (with Roger Howe) The unitary representation theory of GL(n) of an infinite discrete field, Israel J. Math. 67 (1989), no. 1, 67-81.
  28. (with Shmuel Weinberger) An equivariant Novikov conjecture, With an appendix by J. P. May, K-Theory 4 (1990), no. 1, 29-53.
  29. The KO-assembly map and positive scalar curvature, in Algebraic topology, Poznan, 1989, 170-182, Lecture Notes in Math., 1474, Springer, Berlin, 1991.
  30. (with Shmuel Weinberger) Higher G-signatures for Lipschitz manifolds, K-Theory 7 (1993), 101-132.
  31. C*-algebras and Mackey's theory of group representations (in "C*-algebras: 1943-1993 [San Antonio, TX, 1993]", Contemp. Math., 167, Amer. Math. Soc., 1994.)
  32. (with Siegfried Echterhoff) Fine structure of the Mackey machine for actions of abelian groups with constant Mackey obstruction, Pacific J. Math. 170, no. 1 (1995), 17-52.
  33. (with Shmuel Weinberger) Higher G-indices and applications, Annales Scientifiques de l'École Normale Supérieure (4) 21 (1998), 479-495.
  34. Brown-Douglas-Fillmore theory, an article from the Encyclopaedia of Mathematics (2002).
Some recent publications:
  1. "Algebraic K-Theory and its Applications," Graduate Texts in Mathematics, vol. 147, Springer-Verlag, New York, 1994 (approx. 400 pages). ISBN 0-387-94248-3. Corrected second printing, 1996. For owners of the first printing, here is a list of the mistakes and misprints (in dvi format) that have been corrected in the second printing. This list is also available in pdf format. For owners of both printings, here are some additional errata in dvi format or in pdf format.
  2. "Novikov Conjectures, Index Theorems and Rigidity," co-edited with Steve Ferry and Andrew Ranicki, London Math. Soc. Lecture Notes, vols. 226 and 227 (approx. 380 pages each), Cambridge Univ. Press, 1995. ISBN 0-521-49796-5 and ISBN 0-521-49795-7. Some errata are available.
  3. (with Stephan Stolz), "A "stable" version of the Gromov-Lawson conjecture," in "The Čech Centennial: A Conference on Homotopy Theory," M. Cenkl and H. Miller, eds., Contemp. Math., vol. 181, Amer. Math. Soc., 1995, pp. 405-418.
  4. (with Ronald L. Lipsman), "The behavior of Fourier transforms on nilpotent Lie groups," Trans. Amer. Math. Soc. 384 (1996), 1031-1050.
  5. "Lajos Pukánszky: In memorium," Notices Amer. Math. Soc. 45 (1998), 492. The whole collection of memorial articles in this issue of the Notices is available here.
  6. "The algebraic K-theory of operator algebras." Appeared in K-Theory 12 (1997), 75-99. The dvi file uses the xypic-fonts. The paper is also available in postscript format (approx. 290kb).
  7. a "featured review" of papers by Nest and Tsygan on algebraic index theorems, Math. Rev. 96j:58163ab.
  8. "Behavior of K-theory under quantization," in Operator Algebras and Quantum Field Theory, ed. by S. Doplicher, R. Longo, J. E. Roberts, and L. Zsido, International Press, 1997, pp. 404-415. The paper is also available in postscript format (approx. 160kb).
  9. "Reflections on C. T. C. Wall's work on cobordism." appeared in "Surveys on Surgery Theory", vol. 2, Ann. of Math. Studies, vol. 149.
  10. Notes for lectures at the Summer Research Conference on Algebraic K-Theory at Seattle in July, 1997. A more complete version that appeared in the proceedings of the conference, PSPUM/67, AMS, 1999, pp. 231-248, is also available.
  11. "The K-homology class of the Euler characteristic operator is trivial," Proc. Amer. Math. Soc. 127 (1999), pp. 3467-3474.
  12. (with Stephan Stolz), "Metrics of positive scalar curvature and connections with surgery." appeared in "Surveys on Surgery Theory", vol. 2, Ann. of Math. Studies, vol. 149.
  13. "The K-homology class of the equivariant Euler characteristic operator." The paper is also available in postscript format (approx. 230kb). This paper is now obsolete; see item #27 below.
  14. "The G-Signature Theorem Revisited." Appeared in Tel Aviv Topology Conference: Rothenberg Festschrift, M. Farber, W. Lück, and S. Weinberger, eds., Contemp. Math. 231, Amer. Math. Soc., 1999, pp. 251-264. The paper is also available in pdf format (approx. 280kb).
  15. "Surgery theory today: what it is and where it's going." appeared in "Surveys on Surgery Theory", vol. 2, Ann. of Math. Studies, vol. 149.
  16. A review of Characters of Connected Lie groups by Lajos Pukánszky, appeared in the book reviews section of the Bulletin of the London Math. Soc, 2001.
  17. A minicourse on applications of non-commutative geometry to topology, slides for lectures at the CMI Instructional Symposium and AMS Summer Research Conference on Noncommutative Geometry at Mount Holyoke College, June, 2000. (pdf format, approx 900kb)
  18. A history of non-commutative harmonic analysis in 20th century Hungarian mathematics, for A Panorama of Hungarian Mathematics in the XXth Century, edited by John Horvath, published by Springer, 2006, in the series "Bolyai Society Mathematical Studies". (pdf format, approx 250kb)
  19. A Guide to MATLAB, for Beginners and Experienced Users, Cambridge University Press, 2001. 2nd edition in press, 2005.
  20. Some examples of mathematical analysis applied to Talmud study. Some of this article is in Hebrew, but most of the important sections are translated. To have the Hebrew display correctly, set the font encoding to "Hebrew visual", ISO-8859-8.
  21. The Yamabe invariant for non-simply connected manifolds, with Boris Botvinnik, Journal of Differential Geometry 62 (2002), no. 2, 175-208. (pdf format, approx 280kb)
  22. Groupoid C*-algebras and index theory on manifolds with singularities (PDF format, approx 220kb), Geometriae Dedicata 100 (2003), no. 1, 65-84. A lecture on this material is also available on the MSRI website in streaming video (with the slides in a separate window).
  23. Preliminary copy of several chapters of a book on noncommutative geometry applied to topology, based on item 17 above.
  24. Slides from a talk at the Varieties Conference in honor of Blaine Lawson, June, 2002, on "Recent progress on the Gromov-Lawson Conjecture".
  25. Positive scalar curvature for manifolds with elementary abelian fundamental group (pdf format, approx 175kb), with Boris Botvinnik, Proceedings of the Amer. Math. Soc. 133 (2005), no. 2, 545--556. Also available as a dvi file.
  26. The equivariant Lefschetz fixed point theorem for proper cocompact G-manifolds (pdf format, approx 300kb), with Wolfgang Lück, Proc. Trieste Conf. on High-Dimensional Manifolds, 2001, T. Farrell, L. Göttsche, and W. Lück, eds., World Scientific, 2003.
  27. Equivariant Euler characteristics and K-homology Euler classes for proper cocompact G-manifolds (pdf format, approx 380kb), with Wolfgang Lück, Geometry and Topology 7 (2003), 569-613. Also available in postscript format.
  28. Slides for a talk on "A selective history of the Stone-von Neumann theorem" at the AMS meeting in Baltimore, January, 2003 (special session in honor of the 100th birthdays of Stone and von Neumann). A more detailed version is available as item #31 below.
  29. Slides for a talk on "Another look at the Universal Coefficient Theorem for Ext" at the AMS meeting in Baltimore, January, 2003 (special session in honor of Larry Brown's 60th birthday).
  30. K-theory and geometric topology, a survey article from the "Handbook of Algebraic K-theory", edited by Eric Friedlander and Dan Grayson, Springer, 2004, pp. 577-610. Published version now available online.
  31. A Selective History of the Stone-von Neumann Theorem (pdf format, approx 340kb), in Operator algebras, quantization, and noncommutative geometry, Contemp. Math., 365, Amer. Math. Soc., Providence, RI, 2004, pp. 123-158.
  32. T-duality for torus bundles via noncommutative topology, with Varghese Mathai, Comm. Math. Physics 253 (2005), no. 3, 705-721.
  33. The signature operator at 2, with Shmuel Weinberger, Topology 45 (2006), no. 1, 47-63.
  34. Comparison Between Algebraic and Topological K-Theory for Banach Algebras and C*-Algebras, a survey article from the "Handbook of Algebraic K-theory", edited by Eric Friedlander and Dan Grayson, Springer, 2004, pp. 843-874. Published version now available online.
  35. A K-theory perspective on T-duality in string theory, slides for a talk at the Great Lakes K-theory Conference, X. This talk is based on the material of #32 above.
  36. On mysteriously missing T-duals, H-flux and the T-duality group, with Varghese Mathai, to appear in "Proceedings of the XXXIII International Conference of Differential Geometric Methods in Mathematical Physics" (August 2005), editors Mo-Lin Ge and Weiping Zhang, World Scientific 2006.
  37. Slides and homework exercises from the Oberwolfach Seminar on Topological K-Theory of Noncommutative Algebras and Applications.
  38. T-duality for torus bundles with H-fluxes via noncommutative topology, II: the high-dimensional case and the T-duality group, with Varghese Mathai, Advances in Theoretical and Mathematical Physics 10 (2006), no. 1, 123-158.
  39. An analogue of the Novikov Conjecture in complex algebraic geometry, Trans. Amer. Math. Soc. 360 (2008), no. 1, 383-394.
  40. A review of The Novikov Conjecture: Geometry and Algebra, by Matthias Kreck and Wolfang Lück, Bull. Amer. Math. Soc. 43 (2006), 599-604.
  41. D-branes, RR-fields and Duality on Noncommutative Manifolds, with Jacek Brodzki, Varghese Mathai, and Richard J. Szabo, Comm. Math. Physics 277 (2008), no. 3, 643-706.
  42. Manifolds of positive scalar curvature: a progress report, in Surveys in Differential Geometry, vol. XI: Metric and Comparison Geometry, ed. by Jeffrey Cheeger and Karsten Grove.
  43. Applications of noncommutative topology in geometry and string theory, informal notes from a course at the Institut Henri Poincaré, January, 2007.
  44. The numbers in Numbers, a statistical analysis of the census data in the Biblical book of Numbers. Set the font encoding to Unicode (UTF-16) if you want the Hebrew to display properly.
  45. Notes from a talk at Oberwolfach on #40 above.
  46. Slides from a talk at a Special Session at the San Deigo AMS meeting, January 2008: "First steps towards a noncommutative theory of nonlinear elliptic equations".
  47. Noncommutative variations on Laplace's equation, based in part on #45 above, in Analysis and PDE, 1 (2008), no. 1, 95-114, arXiv:0802.4033.
  48. Noncommutative correspondences, duality and D-branes in bivariant K-theory, with Jacek Brodzki, Varghese Mathai, and Richard J. Szabo, Adv. in Theoretical and Math. Phys. 13 (2009), no. 2, 497-552, arXiv:0708.2648.
  49. The SCHOL Project at the University of Maryland: Using Mathematical Software in the Teaching of Sophomore Differential Equations, with Ronald L. Lipsman and John E. Osborn, J. Numer. Anal. Indust. Appl. Math. 3, no. 1-2, 81-103.
  50. A noncommutative sigma-model, with Varghese Mathai, J. of Noncommutative Geometry 5 (2011), no. 2, 265-294.
  51. Notes and slides from course at the Buenos Aires Winter School on Noncommutative Geometry, July-August 2010, to appear in Clay Math. Proc. 16 (2012), 93-129.
  52. Introduction to Proc. Symp. Pure Math., vol. 81, "Superstrings, geometry, topology, and C*-algebras", Amer. Math. Soc., 2010.
  53. (with Stefan Mendez-Diez) K-theoretic matching of brane charges in S- and U-duality, arxiv:1007.1202, Adv. Theor. Math. Phys. 16 (2012), no. 6, 1591-1618.
  54. Slides from a lecture series at RIMS, Kyoto, February, 2011, on Dualities in field theories and the role of K-theory.
  55. Dualities in field theories and the role of K-theory, arxiv:1107.5015, appeared in Noncommutative Geometry and Physics, 3, ed. by Giuseppe Dito et al., World Scientific, 2013, 485-506.
  56. Some work of Stefan Banach and the mathematics it has generated, Wiadomości Matematyczne 48 (2012), no. 2, 217-212. (Special issue about Polish mathematicians for the 6th European Congress of Mathematics, 2012.)
  57. The Künneth Theorem in equivariant K-theory for actions of a cyclic group of order 2, Alg. and Geom. Topology 13 (2013) 1225-1241, arXiv:1208.6355.
  58. (with Yehoshua Dan Agassi) Flux quantization for a superconducting ring in the shape of a Möbius band, arXiv:1301.2743.
  59. Slides for a minicourse at NCGOA 13, Vanderbilt University, May, 2013, on "Variants of K-theory and connections with noncommutative geometry and physics".
  60. (with Charles Doran and Stefan Mendez-Diez) T-duality for orientifolds and twisted KR-theory, Lett. Math. Phys. 104 (2014), 1333-1364, arXiv:1306.1779, doi: 10.1007/s11005-014-0715-0.
  61. (with Varghese Mathai) T-duality for circle bundles via noncommutative geometry, arXiv:1306.4198, Adv. Theor. Math. Phys. 18 (2014), no. 6, 1437-1462, doi: 10.4310/ATMP.2014.v18.n6.a6.
  62. Levi-Civita's Theorem for noncommutative tori, SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) 9 (2013), 071, 9 pages, doi: 10.3842/SIGMA.2013.071. See also this lecture on this material from the Noncommutative Geometry Festival at TAMU in spring, 2014.
  63. (with Charles Doran and Stefan Mendez-Diez) String theory on elliptic curve orientifolds and KR-theory, arXiv:1402.4885, Comm. Math. Phys. 335 (2015), no. 2, 955-1001. doi: 10.1007/s00220-014-2200-0.
  64. Real Baum-Connes assembly and T-duality for torus orientifolds, J. Geom. and Phys. 89 (2015), 24-31, arXiv:1407.7735, doi: 10.1016/j.geomphys.2014.12.004
  65. Algebraic K-theory and derived equivalences suggested by T-duality for torus orientifolds, J. Pure Appl. Algebra 221 (2017), no. 7, 1717-1728, arXiv:1604.04535.