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Full Name
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Datuashvili Tamar
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| Address | |
| Gogebashvili I passage No. 15, 0179, Tbilisi, Georgia | |
| Phone | |
| (995 32) 22 64 04 | |
| Fax | |
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E-mail
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| Web Page | |
| http://www.rmi.acnet.ge/~tamar | |
| Date Of Birth | |
| 1954-02-16 | |
| Education | |
| School education: 1961-1971 in Tbilisi. University education: 1971-1976 Diploma in mathematics (grade:excellent). State University of Georgia (Tbilisi). 1976-1981: Aspirantura (post-graduate courses) at the Mathematical Institute of the Georgian Academy of Sciences. Subjects of examinations: Mathematics, English, Philosophy (grade: excellent). 1982: Candidate of Physical and Mathematical Sciences, defense of candidate thesis at St. Petersburg (formerly Leningrad) University. Title of Candidate thesis: On the homological dimension of rings and categories. Adviser: Prof. H. Inassaridze, at this time corresponding, now full member of Georgian Acad. Sci. 2006: Doctor of Physical and Mathematical Sciences, defense of degree at Tbilisi State University. Title of Doctoral thesis: Categorical, homological and homotopical properties of algebraic objects. | |
| Position | |
| 1977-1978: Invited teacher at the Tbilisi State University, faculty of Mechanics and Mathematics. 1981-1986 Junior scientist, 1986-1990 Scientist, 1990- Senior scientist at the A. Razmadze Mathematical Institute of the Georgian Academy of Sciences. 1999- Invited lecturer at the Tbilisi State University, faculty of Mechanics and Mathematics. | |
| Publications | |
| T. Datuashvili 1. On the cohomological dimension of categories, Bull. Georgian Acad. Sci., 88 ( 1977), No.1, 17-20. 2. On the cohomology of categories, Proc. Math. Inst. Georgian Acad. Sci., LXII ( 1979), 28-37. 3. On Hilbert’s theorems for polinomial extensions of additive categories, Abstracts of the talks of the VIII Conference of Georgian Mathematicians, Kutaisi, 1979. 4. On the computation of the global homological dimension of certain linear topological matrix rings, Abstarcts of the All-Union Symposium on the Theory of Rings, Algebras and Modules,1980, Kishenev (Moldavia). 5. On the global homological dimension of extensions of rings, Bull.Georgian Acad. Sci. 100 (1980), No. 2, 301-304. 6. On the global homological dimensions of trivial linear topological extensions of linear topological rings, Bull. Georgian Acad. Sci. 100 (1980), No.3, 537-540. 7. On the homological dimension of extensions of abelian categories and rings, Bull. Georgian Acad. Sci. 101 (1981), No.1, 37-40. 8. On the homological dimension of extensions of abelian categories, Proc. Math. Inst. Georgian Acad. Sci. LXX (1982), 24-41. 9. The global homological dimension of trivial linear topological extensions of rings, Proc. Math. Inst. Georgian Acad. Sci. LXXIV ( 1983), 26-38. 10. Coherence of nontrivial extensions of abelian categories, Proc. Math. Inst. Georgian Acad. Sci. 91 ( 1988), 3-11. 11. Cohomology of internal categories in categories of groups with operations, Proc. Conf. Categorical Topology, Prague 1988, World Scientific, 1989, 270-283. 12. Homological dimension of extensions of abelian categories and rings, Lecture Notes in Math. 1437 ( 1990), 1-35. 13. Cohomologically trivial internal categories in categories of groups with operations, Applied Categorical Structures, 3 (1995), No.3, 221-237. 14. Whitehead homotopy equivalence and internal category equivalence of crossed modules in categories of groups with operations, Collected papers on K-theory and Categorical Algebra, Proc. A.Razmadze Math Inst. Acad.Sci. Georgia, 113 (1995), 3-30. 15. Kan extensions of internal functors.Algebraic approach, Georgian Mathematical Journal, 6 (1999), No.2, 127-148. 16. Category Cohomology, An article contributed to Encyclopaedia of Mathematics Supplement II, Kluwer Academic Publishers (2000), 153, 111. 17. Diagram, An article contributed to Encyclopaedia of Mathematics Supplement II, Kluwer Academic Publishers (2000), 153, 112. 18. Categorical properties of Mac Lane – Whitehead constructions, Abstracts of the talks of the International Meeting in Category Theory, Como (Italy), 2000. 19. (with T.Pirashvili), On (Co)Homology of 2-types and crossed modules, J. Algebra, 244 (2001), 352-365. 20. Kan extensions of internal functors. Nonconnected case, J. Pure Appl. Algebra, 167 (2002), 195-202. 21. (with F.W.Bauer), Closed model category structures on the category of chain functors, Topology & its Applications, 131(2003),101-128. 22. Central series for groups with action and Leibniz algebras, Georgian Mathematical Journal, 9(2002), No.4, 671-682. 23. Witt’s theorem for groups with action and free Leibniz algebras, Georgian Mathematical Journal, 11 (2004), No.4, 691-712. 24. ( with F.W. Bauer) The existence of certain (co-) limits in the category of chain functors, Journal of Algebra and Its Applications, vol. 5, No. 3 (2006) 1-23. 25. (with J.M. Casas) Noncommutative Leibniz – Poisson algebras, 24 pages, to appear in Communications in Algebra, 34 (2006), No. 7, 24p. 26. (with F.W. Bauer) Simplicial closed model category structures on the category of chain functors, 26 pages,to appear in Homology, Homotopy and its Applications. 27. (with J.M. Casas and M. Ladra) Actors in categories of interest, 22 pages, submitted for publication. 1-10 in Russian, 10-27 in English. | |
| Conferences,contacts,other scientific and educational activities | |
| Participation In Conferences and Seminars: Georgian Republican Conference of Young Scientists in Mathematics and Mechanics, 1976, Tbilisi. Georgian Republican Conference of Mathematicians 1981, Batumi. Georgian Republican Conference of Mathematicians 1986, Kutaisi. All-Union Symposium on the Theory of Rings, Algebras and Modules,1980, Kishenev (Moldavia). International Conference in Categorical Topology, 1988, Prague (Czechoslovakia). International Meeting in Category Theory, 1989, Bangor (UK). International Conference in Category Theory, 1990, Como (Italy). International Conference in Category Theory, 1991, Montreal (Canada). Seminars in Algebra and Topology at Frankfurt University, 1993 (Germany). European Colloquim of Category Theory, 1994, Tours (France). Conference in the History of Mathematics, 1994, Tbilisi (Georgia). Seminar in Algebraic K-Theory, Groups, and Categories, 1995, Bangor (UK) Homologie et BBQ, 1995, Tours (France). Summer Meeting in Category Theory, 1995, Cambridge (UK). Summer School in Categorical Topology, 1995, Alle-sur-Semois (Belgium). Congress of Georgian Mathematicians, 1997, Tbilisi Georgia). International Conference in Category Theory, 1999, Coimbra (Portugal). School in Category Theory and Applications, 1999, Coimbra (Portugal). CATOP 2000, International Conference, 2000, Fribourg (Switzerland). “Up to Homotopy”, International Conference, 2000, Luminy (France). International Meeting in Category Theory, 2000, Como (Italy). Seminar at IRMA (Institut de Recherche Mathematique Avancee), 2001, Strasbourg (France). Seminars in Category Theory at the Catholic University of Louvain 2002 (Belgium). Conference in Algebra Dedicated to the Jubilee of Prof. H. Inassaridze, 2002, Tbilisi (Georgia). III Seminario de Categorias y Aplicaciones, 2005, Santiago de Compostela (Spain). IV Congress of Georgian Mathematicians, 2005, Tbilisi (Georgia). Universities Visited 1993: (Oct., Nov.) Guest at the University of Frankfurt (Germany), (Prof.Dr. F.W. Bauer, DAAD Fellowship). 1995: (Apr., May) Guest at the School of Mathematics, North Wales University, Bangor (UK), (prof.R. Brown, INTAS programm). 1995: (May- August) Guest at the Tours University (France), (Prof.P. Damphousse). 1999: (August) Guest at the Strasbourg University (France), (Prof..J.-L. Loday). 2000-2001: (Dec.-April) Guest at the University of Frankfurt (Germany), (Prof. Dr. F.W.Bauer, DAAD Fellowship, DFG). 2001: (March) Guest at the Strasbourg University (France), (Prof.J.-L. Loday). 2002: (April-July) Guest at the Catholic University of Louvain (Belgium), (Prof. Fr. Borceux). 2003: (July-September) Guest at the University of Frankfurt (Germany), (Prof.Dr. F. W. Bauer, DFG). 2004: (June-September) Guest at the University of Vigo at Pontevedra (Spain), (Prof. J.-M.Casas). 2005: (July-September) Guest at the University of Vigo at Pontevedra (Spain), (Prof. J.-M. Casas). | |
| Participation in Grant Projects | |
| Languages | |
| Georgian, Russian, English, German. | |
| Scientific interests | |
| Category Theory, Homological Algebra, Homotopical Algebra, Universal Algebras | |
| Current scientific activities | |
| Together with F.W. Bauer we constructed a certain approximation to the simplicial model structure on the category of chain functors. Together with J.M. Casas and M. Ladra we defined actors and general actor objects in categories of interest. We gave the construction of general actor objects and gave the necessary and sufficient conditions for the existence of actors. We defined subcategories of the categories of associative, associative commutative and Leibniz algebras, where actors always exist. We proved that in the category of precrosseed modules within the category of groups actor objects always exist. The existence theorems of actors in the concrete type of algebraic categories are obtained. | |
| Future work plans | |
| To continue the study of homotopical properties of the category of chain functors. To develop homology theory in the category of groups with action on itself. To study universal central extensions of special type of objects in this category. To apply these results and the ones obtained by me earlier (which gave the solutions to the two problems of J.-L. Loday) to the solution of the third problem of Loday, which leads us to a new notion of Leibniz K-theory of a ring. To define subcategories of well-known algebraic categories, where actors always exist. It is desirable to find the constructions of actors in the corresponding categories. | |
| Department | |
| Theoretical Foundations in Mathematics |