TORNIKE KADEISHVILI

Curriculum Vitae

tel.:

+995/232/233-24-29 (home)

595596442 (Mob)

e-mail: kade@rmi.ge

EDUCATION

1966 – 1971 Faculty of Mechanics and Mathematics of Tbilisi State University

1971 - 1974 Post graduate student at Tbilisi State University

SCIENTIFIC DEGREES

1980 Candidate of Sciences (Ph.D.) at Tbilisi State University, " On the Homology Theory of Fibrations", supervisor Prof. N. Berikashvili

1994 Doctor of Sciences (Habitation) at Tbilisi State University "A(∞)-algebra Structure in Cohomology and Rational Homotopy Type".

POSITIONS HELD AND ACADEMIC EXPERIENCE

1974 - Present Employ of Razmadze Mathematical Institute of Georgian Academy of Sciences. Present position – Chairman of Scientific Council of the Institute and Head of the Department of Geometry and Topology,

1992 -1996 Docent of Georgian Technical University

1996 - Present Professor of Georgian Technical University

2008 – Present Lecturer at ISET

PRIZES AND AWARDS

1987 Fellowship from Alexander von Humboldt Foundation, Germany

1995 A. Razmadze Prize of the Georgian Academy of Sciences

2008 Senior Associate of the International Centre for Theoretical Physics, Trieste, Italy

GRANTS

1993 Research Grant from ISF (George Soros Foundation)

2000 Research Grant from CRDF (US Civilian Research & Development Foundation) Some New Aspects of Obstruction and Cobordism Theories, Award GM1-2083

2000 Research Grant from INTAS Linear Algebraic Groups and Related Linear and Homological Structures, Award 99-00817

2006 Research Grant from GNSF (Georgian National Science Foundation) New models of Topological Staces and Fibrations and their Applications in Homotopy Theory, GNSF/ST06/3-007

2008 Lecturing Grant from GNSF SP09

2009 Research Grant from GNSF, Models of Topological Spaces Based on New Cochain Operations and their Applications in Homology and Homotopy Theories, Award GNSF / ST08 / 3 - 398

2009 Grant from PEER – Partnership for Economical Education and Research

2012 Grant from PEER

2013 Research Grant from GNSF, On the Obstruction Theories for Serre Fibrations, Iterated Loop Spaces and High Order Homotopy Algebras,. Award FR/37/5-103/12

WISITING POSITIONS

1985, 3 months International Banach Center, Warsaw

1986, 3 months University UNAM, Mexico

1987, 12 months Heidelberg University, Germany

1991, 12 monthsHeidelberg University, Germany

2000, 3 months Sevilla University, Spain

2001, 6 months Sevilla University, Spain

2001, 3 months Sevilla University, Spain

2002, 1 month Institute Fourier, Universite de Grenoble, France

2003, 3 months Institute Fourier, Universite de Grenoble, France

2005, 1 month Institute Fourier, Universite de Grenoble, France

2005, 2 months International Centre for Theoretical Physics, Trieste, Italy

2006, 1 month International Centre for Theoretical Physics, Trieste, Italy

2007, 1 month North Carolina State University, USA

2008, 1 month International Centre for Theoretical Physics, Trieste, Italy

2009, 1 month International Centre for Theoretical Physics, Trieste, Italy

2010, 2 months International Centre for Theoretical Physics, Trieste, Italy

2012, 1 month International Centre for Theoretical Physics, Trieste, Italy

2014, 1 month International Centre for Theoretical Physics, Trieste, Italy

PARTICIPATION IN CONFERENCES

1983 – Topological Conference, Hungary

1985 - Topological Conference, Oberwolfach, Germany

1986 - Topological Conference, Oberwolfach, Germany

1988 - Topological Conference, Blauboiron, Germany

1988 - Topological Conference, Oberwolfach, Germany

1989 - Topological Conference, Check Republic

1990 - Topological Conference, Spain.

1994 - 2nd Gauss Symposium, Muenchen, Germany

1996 - Topological Conference Heidelberg, Germany

1998 - Topological Conference Anger, France

1998 - International Congress, Berlin, Germany

1999 - French-Georgian Topological Conference, Strasbourg, France

2000 - Conference ‘’Up to Homotopy’’ Lumini, France

2003 - Joint Conference of AMS and RMS, Sevilla, Spain

2007 - Higher Structures in Geometry and Physics, Paris

2007 - Algebraic Topology: Old and New, M. Postnikov Memorial Conference, Poland

2008 – Director of “Summer School and Conference Mathematics, Algorithms and Proofs” ,

International Centre for Theoretical Physics (ICTP), Trieste, Italy.

2009 - Summer School and Advanced Workshop on Trends and Developments in Linear

Algebra, ICTP, Trieste, Italy.

2010 - Summer School and Conference on Hodge Theory and Related Topics, ICTP, Trieste,

Italy.

2013 - Topological Materials: New Physics and Gateway to New Critical Technologies,

Turkay.

2014 – Conference “Lie Groups, Differential Equations and Geometry”, Palermo, Italy.

ORGANIZING CONFERENCES

1999 - Coordinator of UNESCO Conference Modern "Mathematical Methods and their

Applications", October 9-15, 1999, Tbilisi, Georgia

2000 - Coordinator of UNESCO Conference "Algebraic models for topological spaces

and their applications", September 2-9, 2000, Tbilisi, Georgia

2002 - Coordinator of UNESCO Conference "Algebraic models for topological spaces

and fibrations", September 21-27, 2002, Tbilisi, Georgia

2004 - Coordinator of UNESCO Conference "Algebraic models for topological spaces

and fibrations", September 13-18, 2004, Tbilisi, Georgia

2008 – Director of “Summer School and Conference Mathematics, Algorithms and Proofs” ,

International Centre for Theoretical Physics, Trieste, Italy, 11-29 August.

2009 – Vice Chairman of Organizing Committee of CONGRESS OF MATHEMATICIANS OF GEORGIA October 9 to 12, Batumi

2010 – Vice Chairman of Scientific Committee of First Annual Conference of Georgian Mathematical Union, September 12 to 19, Batumi

2010 – Coordinator of Workshop of “Universal Algebra and its Applications” by Georgian National Science Foundation, September 20-26, Batumi

2011 – Organizer of the Conference “ Advances and Perspectives of Basic Sciences in Caucasus and Central Asian Region”, Tbilisi, November 1-3.

2011 – Coordinator of INTERNATIONAL CONFERENCE MODERN ALGEBRA AND ITS APPLICATIONS, September 19-25, 2011, Batumi, Georgia.

MEMBERSHIPS

1989 Member of American mathematical Society

1998 Vice president of Georgian Mathematical Union.

2004 Member of Governmental Commission for Reforming the Science in Georgia

2013 Member of Consulting Group of Georgian Ministry of Education and Sciences

2014 Member of Scientific Board of Georgian Ministry of Education and Sciences.

Member of the editorial board of “Proceedings of A. Razmadze Mathematical Institute”

Member of the editorial board of “Georgiam Mathematical Journal”

RESEARCH INTERESTS

Algebraic Topology: Homology Theory of Fibrations, Rational Homotopy Theory,

Algebraic Models of Topological Spaces and Fibrations, A(infty)-algebras, Operads, Cohomological Physics, String Theory

PUBLICATIONS

Monograph

1.A(¥ )-algebra Structure in Cohomology and Rational Homotopy Type, Pros. of Tbil. Mat. Inst., 107, 1993, 1-94.

Articles

2. T. Kadeishvili, On the Homology Theory of Fibrations, Bull. of Georg. Acad. Sci.,77, 2, 197, 309-312.

3. T. Kadeishvili, On the Differentials of Spectral Sequence of Fiber Bundle,Bull. of Georg. Acad. Sci., 82, 1976, 285-288.

4*. T. Kadeishvili, On the Homology Theory of Fibrations, Russian Math. Surveys, 35, 3, 1980, 231-238.

5. T. Kadeishvili, Algebraic Structure in Homology of an A(¥ )-algebra, Bull. of Georg. Acad. Sci., 108, 2, 1982, 309-312.

6. T. Kadeishvili, A(¥ )-algebra Structure in Cohomology and Rational Homotopy Groups, Proc. Conf. in Oberwolfach 01.09-06.09, 1985.

7. T. Kadeishvili, The Category of Differential Coalgebras and the Category of A(¥ )-algebras, Proc. of Tbil. Math. Inst., 83, 1986, 26-45.

8. T. Kadeishvili, Twisted Tensor Products for the Categories of A(¥ )-algebras and A(¥ )-modules,Proc. of Tbil. Math. Inst., 83, 1986, 26-45.

9*. T. Kadeishvili, Predifferential of a Fiber Bundle, Russian Math. Surveys,41, 6, 1986, 135-147.

10. T. Kadeishvili, Functor D for the Category of A(¥ )-algerbas, Bull. of Georg. Acad. Sci., 125, 2, 1987, 273-276.

11. T. Kadeishvili, The A(¥ )-algebra Structure and Cohomology of Hochschild and Harrison, Proc. of Tbil. Math. Inst., 91, 1988, 19-27, math. AT/0210331.

12. T. Kadeishvili, A(¥ )-algebra Structure in Cohomology and Rational Homotopy Type, Forschungs swerpunkt Geometrie, Universitaet Heidelrg, Math. Inst., Heft 37, Oktober, 1988, 1-64.

13. T. Kadeishvili, Realization of Maps in the Rational Homotopy Theory. Bull. Acad. Sci. of Georgia, 139, 2, 1990, 261-264.

14*. J. Huebschmann and T. Kadeischvili, Small Models for Chain Algebras. Math. Zeitschrift, 207, 1991, 245-280.

15. T. Kadeishvili, Attaching Cells and the Rational Homotopy Type. Topologie und Nichtcomutative Geometrie, Universitaet Heidelberg, Math. Inst., Heft 37, 1992, 1-19.

16. T. Kadeishvili, On the Sphericaly Generated Spaces, Symposia Gaussiana, Conf. A, W. de Gruyter, Berlin, 1995, 491-498.

17. T. Kadeishvili et al., On the Obstruction Functor, Bull. of Georg. Acad.Sci. , 153, 2, 1996, 172-176.

18. T. Kadeishvili and S. Saneblidze, On a multiplicative model of a fibration. Bull. Georg. Acad. Sci. 153,3, 1996, 345-346.

19. T. Kadeishvili and S. Saneblidze, Iterating the bar construction. Bull. Georg. Acad. 154,3 1996, 338-340.

20. T. Kadeishvili, DG Hopf Algebras with Steenrods i-th coproducts. Bull. Georgian Acad. Sci. 158,2, 1998, 203-206.

21. T. Kadeishvili and S. Saneblidze, The cobar construction as a cubical complex. Bull. Georgian Acad. Sci. 158,3, 1998.

22*. T. Kadeishvili and S. Saneblidze. Iterating the bar construction. Georgian Math. J. 5, 1998, 441--452.

23. T. Kadeishvili and S. Saneblidze, Permutahedral Complex Modeling 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.

24. T. Kadeishvili, DG- Hopf algebras with Steenrod I-th coproducts, Proc. A. Razmadze Math. Inst. 119 (1999), 155-164.

25. T. Kadeishvili and S. Khazhomia, Simplicial cutting of a cubical set, Bull. Georgian. Acad. Sci., 167 , N2, 2003, 205-209.

26*. T. Kadeishvili, Cochain operations defining Steenrod $\smile_i$-products in the bar construction, Georgian Math. Journal, v.10, n. 1, 2003, 115-125, preprint at math.AT/0207010.

27. T. Kadeishvili, Measuring the noncommutativity of DG-algebras, Journal of Mathematical Sciences, 119 (4): 494-512, February 2004.

28*. T. Kadeishvili and S. Saneblidze, A cubical model for a fibration, Jornal of Pure and Appl. Algebra, 196/2-3, 2005, pp 203-228, preprint at math.AT/0210006.

29*. T. Kadeishvili, On the bar construction of a bialgebra, Homology, Homotopy and Appl., v. 7(2) , 2005, 109-122, preprint at math.AT/0406502.

30. T. Kadeishvili and P. Real, Free resolutions for differential modules over differential algebras, Journal of Mathematical Sciences, v. 43 (2006), 1-16.

31. T. Kadeishvili, Cohomology C∞-algebra and rational homotopy type. Banach Center Publications, v. 85, 2009, 225-240.

32*. T. Kadeishvili, T. Lada, A Small Open-Closed Homotopy Algebra (OCHA), Georgian Math. Journal, v.16, n. 2, 2009, 305—310.

33*. T. Kadeishvili, Twisting Elements in Homotopy G-algebras, Higher Structures in Geometry and Physics. In Honor of Murray Gerstenhaber and Jim Stasheff. Series: Progress in Mathematics, Birkhauser, Vol. 287 (2011), 181-200. arXiv:math/0709.3130.

34. T. Kadeishvili, Twisting Elements da=acup1a, Proc. A. Razmadze Math. Inst., 155 (2011), 13-134.

35. T. Kadeishvili, Homotopy Gerstenhaber Algebras: Examples and Applications, Proc. Int. Conf. MODERN ALGEBRA AND ITS APPLICATIONS, Batumi 2011, v. 2, 27-32.

36. T. Kadeishvili, On cochain operations forming Hirsch algebras, JOURNAL OF MATHEMATICAL SCIENCES, Springer, 2012, Volume 186, Issue 5 (2012), Page 753-755.

DOI: 10.1007/s10958-012-1028-4

37. T. Kadeishvili, Homotopy Gerstenhaber algebras: examples and applications, Journal of Mathematical Sciences, Springer, December 2013, Volume 195, Issue 4, pp 455-459.

38. Tornike Kadeishvili* and Samson Saneblidze, The twisted Cartesian model for the double path fibration, Georgian Mathematical Journal, vol. 22 (2015), N4, De Gruyter. Special issue dedicated to 100 Anniversary of Academician George Chogoshvili, v. DOI 10.1515/gmj-2015-0040

39. T. Kadeishvili, B_∞-algebra Structure in Homology of a Homotopy Gerstenhaber Algebra, in Lie groups, Differential equations, and Geometry, UNIPA Springer Series