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.