Representation theory of Lie groups, C*-algebras, K-theory, topology and geometry of manifolds, index theory of elliptic operators, related areas of mathematical physics.
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 Cech 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.
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 (approx. 675 kb in postscript) 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, to be published by Springer 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, your browser must have Hebrew fonts, which you can install following these instructions. A PDF version (which doesn't require Hebrew fonts) is also available, though not all the Hebrew displays very well.
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, to appear.
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.
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.
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.
37. 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.
38. An analogue of the Novikov Conjecture in complex algebraic geometry, Trans. Amer. Math. Soc. 360 (2008), no. 1, 383-394.
39. A review of The Novikov Conjecture: Geometry and Algebra, by Matthias Kreck and Wolfang Lück, Bull. Amer. Math. Soc. 43 (2006), 599-604.
40. 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.
41. 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.
42. Applications of noncommutative topology in geometry and string theory, informal notes from a course at the Institut Henri Poincaré, January, 2007.
43. The numbers in Numbers, a statistical analysis of the census data in the Biblical book of Numbers.
44. Notes from a talk at Oberwolfach on #40 above.
45. 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".
46. 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.
47. 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.
48. 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.