# Gennadi Kasparov

Professor Emeritus

#### Research Interests

K-theory, operator algebras

#### Publications

K-theoretic index theorems for elliptic and transversally elliptic operators, *Journal of K-theory, to appear.*

(With G. Yu). Groups with coarse positive duality and the Novikov conjecture, preprint, 2005. PDF

(With G. Yu). The coarse geometric Novikov conjecture and uniform convexity. Advances in Math., 206 (2006), 1-56.

(With G. Skandalis). Groups acting properly on "bolic'' spaces and the Novikov conjecture. *Annals of Math.* (2), 158 (2003), 165-206.

(With N. Higson). E-theory and KK-theory for groups which act properly and isometrically on Hilbert space. *Inventiones Math.*, 144 (2001), 23-74.

(With N. Higson and J. Trout). A Bott periodicity theorem for infinite dimensional Euclidean space. *Advances in Math.*, 135 (1998), 1-40.

(With N. Higson). Operator K-theory for groups which act properly and isometrically on Hilbert space. *Electronic Research Announcements of the Amer. Math. Soc.*, 3 (1997), 131-142.

K-theory, group C^{*-algebras, and higher signatures. (Conspectus). In: *Novikov Conjectures, Index Theorems and Rigidity*, eds.: S. C. Ferry, A. Ranicki, J. Rosenberg, Cambridge Univ. Press, 1995, v. 1 (*London Math. Soc. Lect. Notes Series*, v. 226), p.p. 101-146.

(With P. Julg). Operator K-theory for the group SU(n,1). *J. Reine Angew. Math.*, 463 (1995), 99-152.

(With G. Skandalis). Groupes ''boliques'' et conjecture de Novikov. *Compt. Rend. Acad. Sci. Paris*, 319 (1994), Ser. I, 815-820.

Novikov's conjecture on higher signatures: The operator K-theory approach. *Contemporary Math.*, 145 (1993), 79-99.

Relative K-homology and K-homology of an ideal. *K-theory*, 5 (1991), 47-49.

(With P. Julg). L'anneau KK_G( C, C) pour G=SU(n,1). *Compt. Rend. Acad. Sci. Paris*, 313 (1991), Ser. I, 259-264.

(With G.Skandalis). Groups acting on buildings, operator K-theory, and Novikov's conjecture. *K-theory*, 4 (1991), 303-337.

(With G. Skandalis). Groupes agissant sur des immeubles de Bruhat-Tits, K-theorie operatorielle et conjecture de Novikov. *Compt. Rend. Acad. Sci. Paris*, 310, Ser. I, 171-174 (1990).

Equivariant KK-theory and the Novikov conjecture. *Inventiones Mathematicae*, 91 (1988), 147-201.

(With N. V. Gorbachev). On extensions related with group C^*-algebras. *Uspekhi Matem. Nauk*, 40, no. 2 (1985), 173-174; English translation: *Russian Mathematical Surveys*, 40, no. 2 (1985), 213-214.

Operator K-theory and its applications. In: *Itogy Nauki i Tekhniki, Ser. Sovremennye Problemy Matematiki*, v.27, pp. 3-31. Moscow: VINITI 1985.

Operator K-theory and its applications: elliptic operators, group representations, higher signatures, C^*-extensions. In: *Proceedings ICM, Aug. 16-24, 1983 Warszawa*, pp. 987-1000. Warsaw-Amsterdam: PWN-Elsevier Publishers 1984.

Lorentz groups: K-theory of unitary representations and crossed products. *Dokl. Akad. Nauk SSSR*, 275 (1984), 541-545; English translation: *Soviet Mathematics - Doklady*, 29 (1984), 256-260.

The index of invariant elliptic operators, K-theory, and Lie group representations. *Dokl. Akad. Nauk SSSR*, 268 (1983), 533-537; English translation: *Soviet Mathematics - Doklady*, 27 (1983), 105-109.

The operator K-functor and extensions of C^*-algebras. *Izvestiya Akad. Nauk SSSR, Ser. Matem.*, 44 (1980), 571-636; English translation: *Mathematics USSR - Izvestiya*, 16 (1981), 513-572.

Hilbert C^*-modules: theorems of Stinespring and Voiculescu. *J. Operator Theory*, 4 (1980), 133-150.

K-functor in the theory of extensions of C^*-algebras. *Funkc. Analiz i ego Prilozh.* , 13, no. 4 (1979), 73-74; English translation: *Functional Analysis and its Applications*, 13, no. 4 (1979), 296-297.

Topological invariants of elliptic operators. I. K-homology. *Izvestiya Akad. Nauk SSSR, Ser. Matem.*, 39 (1975), 796-838; English translation: *Mathematics USSR - Izvestiya*, 9 (1975), 751-792.

Generalized index of elliptic operators. *Funkc. Analiz i egoPrilozh.* 7, no. 3 (1973), 82-83; English translation: Functional Analysis and its Applications, 7, no. 3 (1973), 238-240.

On the homotopy invariance of rational Pontryagin numbers. *Dokl. Akad. Nauk SSSR*, 190 (1970), 1022-1025; English translation: *Soviet Mathematics - Doklady*, 11 (1970), 235-238.

Invariants of classical lens manifolds in cobordism theory. *IzvestiyaAkad. Nauk SSSR, Ser. Matem.* , 33 (1969), 735-747; English translation: *Mathematics USSR - Izvestiya*, 3 (1969), 695-705.

#### Conference Talks

International Conference Noncommutative Geometry", Vanderbilt University, Nashville, May 2008.

International Conference in honor of Prof. J. Cuntz, Muenster, Germany, September 24 - 27, 2008.

International Symposion, University of Munster, Germany, June 2006

International Conference "Topology, analysis, and applications to mathematical physics," Moscow State University, February 2005

International Conference "Noncommutative Geometry," Vanderbilt University, Nashville, May 2003

International Conference “Quantization and Noncommutative geometry,” MSRI, Berkeley, April 2001

North British Functional Analysis Seminar, Edinburgh, May 2000

International Conference “Noncommutative geometry,” Strasbourg, December 1997

International Conference “E-theory, Quantization, and Deformations” at Dartmouth College, September 1997

International Conference “Operator Algebras and Singular Spaces” at the University Aix-Marseille II, November 1996

Canadian Operator Symposium at the Fields Institute, Waterloo, June 1995

International Conference “Quantized Geometry” at the Ohio State University, Columbus, May 1991

Oberwolfach International Meetings: “Topology,” 1988; “C^*-algebras',” 1991; “Novikov Conjectures, Index Theorems and Rigidity,” 1993; “C^*-algebras',” 1996

International Conference “Topology,” Baku (USSR), October 1987

International Conference “Operator Theory,” Bucharest, August 1985

A 45-minute address at the International Congress of Mathematicians in Warsaw, August 1983

#### Editorships

- Member of the Editorial Board of K-Theory
- Member of the Editorial Board of Journal of Noncommutative Geometry