Gennady Georgievich Kasparov

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Gennadi Georgijewitsch Kasparov ( Russian Геннадий Георгиевич Каспаров , English transcription Gennadi Kasparov ) is a Russian-American mathematician who deals with algebraic topology , operator algebras and their K-theory .

Kasparov studied at Lomonosov University , where he received his doctorate in 1974 with Sergei Petrovich Novikov . In 1984 he completed his habilitation ( Russian doctorate ) at the Academy of Sciences in Kiev . He is the Stevenson Professor of Mathematics at Vanderbilt University .

His first mathematical publication took place as a student in 1969. At the end of the 1970s, he developed a bivariate K-theory of operator algebras, the so-called KK theory (and the KK functor). Among other things, he dealt with the Novikov conjecture of his teacher, the Baum-Connes conjecture (formulated essentially with the help of his KK theory ) (with proofs of special cases with Nigel Higson, among others ) and non-commutative geometry in the sense of Alain Connes .

In 1983 he was invited speaker at the International Congress of Mathematicians (ICM) in Warsaw ( Operator K-theory and its applications: elliptic operators, group representations, higher signatures, C * -extensions ).

Fonts

  • The operator K-functor and extensions of C * -algebras , Izvestija Akad. Nauka SSSR, Ser. Math., Volume 44, 1980, pp. 571-636 (Russian) and Mathematics USSR - Izvestiya, Volume 16, 1981, pp. 513-572 (English), (KK theory)
  • The K-functor in the theory of extensions of C * -algebras , Functional Analysis and Applications, Volume 13, 1979, pp. 296-297
  • Topological invariants of elliptic operators , Part 1: Homology , Izv. Akad. Nauk SSSR Ser. Mat., Volume 39, 1975, pp. 796-838 (Russian) and Mathematics USSR - Izvestiya, Volume 9, 1975, pp. 751-792 (English)
  • Equivariant KK-theory and the Novikov conjecture , Inventiones Mathematicae, Volume 91, 1988, pp. 147-201
  • Novikov's conjecture on higher signatures: The operator K-theory approach , Contemporary Mathematics, Volume 145, 1993, 79-99
  • K-theory, group C * -algebras, and higher signatures , in SC Ferry, Andrew Ranicki , J. Rosenberg (editors) Novikov Conjectures, Index Theorems and Rigidity , London Mathematical Society Lecture Notes Series 226, Cambridge University Press, 1995, volume 1, pp. 101-146
  • with Nigel Higson : E-theory and KK-theory for groups which act properly and isometrically on Hilbert space , Inventiones Math., Volume 144, 2001, pp. 23-74
  • with Georges Skandalis : Groups acting properly on "bolic" spaces and the Novikov conjecture , Annals of Mathematics, Volume 158, 2003, pp. 165-206

Web links

Individual evidence

  1. ^ G. Kasparov - The Mathematics Genealogy Project. Retrieved June 27, 2019 .
  2. ↑ Invariants of classical lens manifolds in cobordism theory , Mathematics USSR - Izvestiya, Volume 33, 1969, pp. 695-705, Russian Izv. Akad. Nauka SSSR, Volume 3, 1969, pp. 735-747
personal data
SURNAME Kasparov, Gennady Georgievich
ALTERNATIVE NAMES Каспаров, Геннадий Георгиевич (Russian)
BRIEF DESCRIPTION Russian-American mathematician
DATE OF BIRTH 20th century