Inassaridze Hvedri

Full Name
Inassaridze Hvedri
Avenue Chavchavadze 75, building 3, apart. 35, Tbilisi 0162, Georgia
995 32 230852, 899 157836
Web Page
Date Of Birth
Born in Paris, France, December 6, 1932. Secondary education at Lycee Claude Bernard, Paris (till 1947) and secondary school in Tbilisi (1947-1950). In 1950-1951 student of Tbilisi State University, physico-mathematical faculty; in 1951 his family was sent for permanent exile to Kazakhstan but was rehabilitated in 1954 (after Stalin’s death). Continued to study in Tbilisi State University and graduated in 1958; 1958-1961 – postgraduate student of A. Razmadze Mathematical Institute of the Georgian Academy of Sciences.
From 1961 – scientific member of A. Razmadze Mathematical Institute. From 1966 – Candidate and from 1970 – doctor of physical and mathematical sciences, confirmed by Highest Certification Commission (VAK) in Moscow. From 1983 – 2001 corresponding member and from 2001- full member of the Georgian Academy of Sciences. 1990-1997 – President of the Georgian National Mathematical Committee. 1990-1991 – deputy of the Parliament of Georgia. Present positions: Head of the Algebra Department of A.Razmadze Mathematical Institute, Professor of Tbilisi State University.
1. Universal functors, Bull. Georgian Acad. Sci. 38, No3 (1965) (in Russian). 2. Extensions of regular semigroups, Bull. Georgian Acad. Sci. 39, No1 (1965) (in Russian). 3. On finite order extensions and remainders of completly regular spaces , Doklady Acad. Nauk USSR 166, No5 (1966). 4. On a generalization of perfect mappings, Doklady Acad. Nauk USSR 168, No2 (1966). 5. Alexander-Kolmogorov cohomology with coefficients in commutative inverse semigroups, Bull. Georgian Acad. Sci. 54, No2 (1969) (in Russian). 6. Exact homology and linking for Steenrod duality, Doklady Acad. Nauk USSR 206, No1 (1972) (in Russian). 7. On exact homology, Proc. A.Razmadze Math. Institute, 41 (1972) (in Russian). 8. Exact homology and Tate cohomology of locally compact zerodimensional groups, Bull. Georgian Acad. Sci. 74, No1 (1974) (in Russian). 9. On algebraic K-functors, Bull. Georgian Acad. Sci. 77, No1 (1975) (in Russian). 10. Generalization of Milnor sequence for inverse limits, Bull. Georgian Acad. Sci. 79, No1 (1975) (in Russian). 11. Homotopy of pseudosimplicial groups, nonabelian derived functors and algebraic K-theory, Matem. Sbornik 98, No3 (1975), 339 – 362. 12. Some topics of homological and homotopical algebra and their applications, Proc. A.Razmadze Math. Institute 48 (1975), 140 pages (in Russian). 13. On Swan-Gersten K-functor K3, Bull. Georgian Acad. Sci. 111, No3 (1983), 29-31 (in Russian). 14. K-theory of special normed algebras, Uspehi Mat. Nauk 40, No4 (1985), 169-170. 15. K-theory of special normed rings, Lecture Notes in Math., Springer verlag, 1437 (1990), 95 -156. 16. On the Steenrod homology of compact spaces, Michigan Math. J. 38, No3 (1991), 323 – 338. 17. Algebraic K-theory, Kluwer Acad. Publishers, Amsterdam, 1995, 440 pages. 18. Nonabelian homological algebra and its applications, Kluwer Acad. Publishers, Amsterdam, 1997, 270 pages. 19. Nonabelian cohomology of groups, Georgian Math. J. 4, No4 (1997), 313 – 332. 20. Nonabelian cohomology with coefficients in crossed bimodules , Georgian Math. J. 4, No6 (1997), 509 – 522. 21. Universal property of Kasparov bivariant K-theory, Bull. Georgian Acad. Sci. 156, No2 (1997), 185 – 189. 22.(with N.Inassaridze) Nonabelian homology of groups, K-theory J. 378 (1999), 1-17. 23.(with N.Inassaridze) New descriptions of the nonabelian homology of groups, Bull. Georgian Acad. Sci. 157, No2 (1998), 196 – 200. 24.(with N.Inassaridze) The second and the third nonabelian homology of groups, Bull. Georgian Acad. Sci. 158, No3 (1998). 25. Algebraic K-theory of normed algebras, K-Theory 21, No 1 (2000), 25-56. 26. Higher nonabelian cohomology of groups, Glasgow Math. J. 44 (2002), 497-520. 27.(with D.Conduché and N.Inassaridze) Mod q cohomology and Tate cohomology of groups, Prepublication 01-29 (2001), Institute de Recherche Mathematique de Rennes. 28.(with D.Conduché and N.Inassaridze) Mod q cohomology and Tate-Vogel cohomology of groups, J. Pure Appl. Algebra 189 (2004), 61-87. 29.(with A.Garzon) Semidirect products of categorical groups. Obstruction theory and derivations, Homology, Homotopy and Applications 3 (1) (2001), 111-138. 30.(with T.Kandelaki) K-theory of stable generalized operator algebras , K-Theory 27 (2002), 103-110. 31.(with A.Garzon and A.del Rio) Derivations of categorical groups, Theory and Applications of Categories 13 (5) (2004), 86-105. 32. More about (co)homology of groups and associative algebras, Homology, Homotopy and Applications 7 (1) (2005), 87-108. 33.(with A.M.Cegarra) Homology of groups with operators, Intern. Math. J. 5 (1) (2004), 29-48. 34. Equivariant homology and cohomology of groups, Topology and its Applications 153 (2005), 66-89. 35.(with D.Arlettaz) Finite K-theory spaces, Proc. Cambridge Phil. Soc. 139 (2005), 261-286. 36.(with T.Kandelaki) Smooth K-theory of locally convex algebras, Trans. Amer. Math. Soc. 2006, (to appear), arXiv: math.KT/0603095.
Conferences,contacts,other scientific and educational activities
Special courses in algebra for students of the faculty of Mechanics and Mathematics of Tbilisi State University. Seminars on Homological Algebra and Algebraic K-theory (A.Razmadze Mathematical Institute). Ph.D students (Thesis defended at Tbilisi State University): T. Datuashvili, J. Gubeladze, G. Janelidze, T. Kandelaki, R. Katamadze, E. Khmaladze, A. Landia, Nguyen Suan Tuyen, A. Patchkoria, B. Patchuashvili, T. Pirashvili, G0. Rakviashvili, E. Rtveliashvili, M. Uridia, Z.Janelidze. Doct. Sc.: J. Gubeladze, G. Janelidze, Nguyen Suan Tuyen, T.Datuashvili. Vice-chairman of the Scientific Committee at Tbilisi State University for awarding the candidate and doctoral degrees in Mathematical Logic, Algebra, Number Theory, Analysis, Geometry and Topology. Founder and Editor-in-Chief (1998-2005) of the mathematical journal “Homology, Homotopy and Applications”. Editor-in-Chief of a new international all electronic journal in mathematics entitled “Journal of Homotopy and Related Structures” (JHRS). Member of the Editorial Board of Georgian Mathematical Journal. Talks at International Conferences, Workshops and Seminars: Workshop at the Mathematical Institute of Warsaw, 1990. Conference in Algebra and Mathematical Logic at the University of Cambridge, 1991. European Congress of Mathematicians, Paris, 1992. Workshop at the University of Wales, Bangor, 1995. International Congress of Mathematicians Berlin, 1998. Conference in Homotopical Algebra, Strasbourg, 1999. Workshop at the University of Granada, 1999. Séminaire de Géométrie Algébrique,Université de Rennes 1, 2001. Séminaire de Géométrie Algébrique, Université Montpellier II, 2001. The Algebra Seminar at the University of Santiago de Compostela, 2001. The Seminar at the University of Vigo, 2001. The Seminar at the University of Lausanne, 2001. The Algebra Seminar at the University of Santiago de Compostela, 2004. Conference in Algebraic Topology, Arolla, Switzerland, 2004. Seminaire de Topologie Algebrique, Universite Paris 13, 2006
Participation in Grant Projects
Awarded by AMS, ISF, INTAS, CRDF, CNRS, INTAS Georgia, NATO and FNRS grants, Razmadze Prize of the Georgian Academy of Sciences, International Kharizmi First Prize of Science and Technology of Iran.
French, English, Russian
Scientific interests
Homological and homotopical algebra, K-theory, non-commutative geometry, category theory, algebraic topology.
Current scientific activities
Has initiated and developed a theory of derived functors and satellites of nonadditive functors with respect to projective classes and presheaves of categories with applications to (co)homology of algebraic systems and K-theory. Has constructed the algebraic K-theory of normed algebras based on Quillen Q-construction and confirmed the Karoubi Conjecture on the isomorphism of algebraic and topological K-functors for a wide class of stable real or complex algebras. Recently has provided a theory of equivariant (co)homology of groups with applications in algebraic K-theory and equivariant cohomology of spaces. With T.Kandelaki he has proved the isomorphism of algebraic and topological K-functors for quasi stable Frechet algebras having a uniformly bounded approximate unit by introducing new topological K-functors called smooth k-functors.
Future work plans
To prove the smooth Karoubi Conjecture for the negative and mod q cases and quasi stable Frechet algebras. To investigate smooth K-functors on the category of real or complex locally convex algebras. To study the smooth homotopy property in non-commutative geometry. To continue the investigation of equivariant (co)homology theory of groups with applications in K-theory.
Theoretical Foundations in Mathematics