CURRICULUM VITAE

Born:  05. 09. 1956

 

Education:

1. 1973 - 1978 Faculty of Mechanics and Mathematics of Tbilisi State University.

2. 1978 - 1982 Post graduate student at A. Razmadze Mathematical Institute of Georgian Academy of Sciences.

 

Degrees:

1. 1984 Candidate of Sciences (Ph.D.) at Tbilisi State University "On the Axiomatic of Homology Theories ".

2. 1995 Doctor of Sciences (Habilitation) at Tbilisi State University "Perturbation and Obstruction Theories in  Fibre Spaces".

 

Employment:

1982 -  till now employ of A. Razmadze Mathematical Institute, Tbilisi:

1982 - 1995 - Scientific researcher

1995 - 2006 - Leader scientific researcher

2006 -  till now Senior scientific researcher.

 

Teaching experiences:

1. 1980 - 1982 courses of Algebra at Tbilisi State University.

2. 1985 - 1989 courses of Algebraic Topology at Tbilisi State University.

3. 1992 - 1995 courses of Algebraic Topology at Tbilisi State University.

4. 2008  courses of Algebraic Topology at Tbilisi State University.

 

Research background and list of publications :

Algebraic Topology:  Homology and Homotopy Theory of Fibrations, Algebraic Models of Topological Spaces and Fibrations, Obstruction Theory.

 

 

1.   Saneblidze, S., On the Steenrod extraordinary homology theory, Bull. Acad. Sci. Georgian  SSR (in Russian), 104 (1981), 281-284.

2.   Saneblidze, S., On the uniqueness theorem for the Steenrod-Sitnikov homology theory on the category of compact Hausdorff  spaces,

                             Bull. Acad. Sci. Georgian SSR (in Russian), 105 (1982), 33-36.

3.   Saneblidze, S., On the homology theory of paracompacta, Bull. Acad. Sci. Georgian SSR  (in Russian), 109 (1983), 477-480.

4.   Saneblidze, S., Extraordinary homology theories of compact spaces, Proc. A. Razmadze Math. Inst. (in Russian), 83 (1986), 88-101.

5.   Saneblidze, S., On the uniqueness theorem for the homology theory of paracompacta, Proc. A. Razmadze Math. Inst. (in Russian), 97 (1992), 53-64.

6.   Saneblidze, S., Functor Dk and rational cohomology algebra of a fiber space, Bull.Acad. Sci. Georgian SSR (in Russian), 128 (1987), 261-264.

7.   Saneblidze, S., Functor D and rational cohomology of a fiber space, Bull. Acad. Sci. Georgian SSR (in Russian), 129 (1988), 17-19.

8.   Saneblidze, S., Homology classification of differential algebras, Bull. Acad. Sci. Georgian  SSR (in Russian), 129 (1988), 241-243.

9.   Saneblidze, S., Obstruction theory in rational homotopy theory, Bull. Acad. Sci. Georgian  SSR (in Russian), 134 (1989), 53-55.

10. Saneblidze, S., Hopf filtered model in rational homotopy theory, Bull. Acad. Sci. Georgian  SSR, 136 (1989), 545-547.

11. Saneblidze, S., On the rational cuplength of certain path spaces, Preprint of A. Razmadze  Math. Inst. (1991), 1-7.

12. Saneblidze, S., The set of multiplicative predifferentials and the rational cohomology algebra of fibre spaces, J. of Pure and Appl. Algebra, 73 (1991), 277-306.

13. Saneblidze, S., Filtered model of a fibration and rational obstruction theory, Manuscripta Math., 76 (1992), 111-136.

14. Saneblidze, S., Obstructions to the section problem in fibre bundles, Manuscripta Math., 81 (1993), 95-111.

15. Saneblidze, S., On the homotopy classification of sections in the free loop fibration, J. of  Pure and Appl. Algebra, 91 (1994), 317-327.

16. Saneblidze, S., Perturbation and obstruction theories in fibre spaces, Proc. A. Razmadze Math. Inst., 111, 1994, 1-106.

17. Saneblidze, S., Lusternik-Schnirelmann category of a weak formal space, Bull. Georgian Acad. Sci., 154 (1996), 351-352.

18. Saneblidze, S. et all, On the Obstruction functor, Bull. Georgian Acad. Sci., 153 (1996), 130-136.

19. Saneblidze, S., Obstructions in a fibration with a weak formal base. Bull. Georgian Acad. Sci., 153 (1996), 199-202.

20. Saneblidze, S., On a multiplicative model of a fibration (with T. Kadeishvili), Bull. Georgian Acad. Sci., 153 (1996), 345-346.

21. Saneblidze, S., Iterating the bar construction (with T. Kadeishvili), Bull. Georgian Acad. Sci., 154 (1996), 338-340.

22. Saneblidze, S., The formula determining an A-coalgebra structure on a free algebra, Bull. Georgian Acad. Sci., 154 (1996), 351-352.

23. Saneblidze, S., Obstructions to the section problem in a fibration with a weak formal base,  Georgian Math. J., 4 (1997), 149-162.

24. Saneblidze, S., Homotopy classification of spaces with fixed Pontrjagin algebra, Bull. Georgian Acad. Sci., 157 (1998), 11-13.

25. Saneblidze, S., Functor D with coefficients in an extraordinary homology theory, Bull. Georgian Acad. Sci., 158 (1998), 211-213.

26. Saneblidze, S. (with T. Kadeishvili), The cobar construction as a cubical complex, Bull. Georgian Acad. Sci., 158 (1998), 17-19.

27. Saneblidze, S. (with T. Kadeishvili), Iterating the bar construction, Georgian Math. J., 5 (1998), 441-452.

28. Saneblidze, S. (with T. Kadeishvili), Permutohedral complex model for the double loop space, Proc. of the International Meeting, ISPM-98,

                              Mathematical Methods in Modern Theoretical Physics, School and Workshop, Tbilisi, Georgia, September 5-18 (1998), 231-236.

29. Saneblidze, S., On the homotopy classification of spaces by the fixed loop space homology,  Proc. A. Razmadze Math. Inst., 119 (1999), 155-164.

30. Saneblidze, S. (with R. Umble), Diagonals on the permutahedra, multiplihedra and associahedra, J. Homotopy, Homology and Appl., 6(1), (2004), 363-411.

31. Saneblidze, S. (with T. Kadeishvili), A cubical model of a fibration, J. Pure and Appl. Algebra, 196 (2005), 203-228.

32. Saneblidze, S. (with R. Umble), The biderivative and A-bialgebras, J. Homology, Homotopy and Appl., 7(2) (2005), 161-177.

33. Saneblidze, S., On derived categories and derived functors,  Extracta Mathematicae,  22 (2007), 315-324.

34. Saneblidze, S., The bitwisted Cartesian model for the free loop fibration, Topology and its Appl., 156 (2009), 897-910.

35. Saneblidze, S., On the homotopy classification of maps,  J. of homotopy and related struct., 4 (2009),  347-357.

36. Saneblidze, S., On the Betti numbers of a loop space,  J. of homotopy and related struct., 5(1),  (2010),  1-13.

37. Saneblidze, S. (with R. Umble),  Matrads,  biassociahedra   and A-bialgebras,  J. Homology, Homotopy and Appl., 13(1),  (2011), 1-57 .

38. Saneblidze, S. (with T. Kadeishvili),  The twisted Cartesian model for the double path space fibration, Georgian Math. J., 22 (4) (2015), 489-508.

39. Saneblidze, S., Filtered Hirsch algebras,  Transactions R.M.I., 170 (2016), 114-136.

 

 

Preprints:

 

1. Saneblidze, S. (with R.  Umble),  A diagonal of associahedra, preprint, math. AT/0011065.

2. Saneblidze, S., The loop cohomology of a space with the polynomial cohomology algebra,  preprint,  math.AT/0810.4531.

3. Saneblidze, S., On the homology theory of the closed geodesic problem,  preprint,  math. AT/1110.5233.

4.Saneblidze,S.(with M. Rivera), A combinatorial model for the path fibration, preprint, math. AT/1706.00983.