Name:           FOMENKO

First name:     ANATOLY

Second name:    TIMOFEEVICH


Adress: Office: Chair of Differential Geometry and Applications,

                Department of Math. and Mech. Moscow State University,

                Moscow, 119992, Russia


Residence:      Russia, Moscow, 119234, Leninskie (Vorobyevy) Gory,                   

                Moscow University.

                Tel: (495)-939-39-40 (office)

                (Fax: (495)-932-89-94 (office)


Date of Birth:  March 13, 1945

Place of Birth: USSR, Donetzk

Marital Status: Married (wife - Tatjana Fomenko)

Education: Mathematics, Moscow University. Faculty

                of Mathematics, June 1967. Thesis: "Cohomology of

                homogeneous spaces"


                Ph.D. in Mathematics, Moscow University, Faculty

                of Geometry and Topology, December 1969. Thesis:

                "Totally geodesic models of the cycles" (The clas-

                sification of totally geodesic submanifolds which

                realize the non-trivial cycles in the Riemannian

                homogeneous manifolds. Differential Geometry and



                Dr. Sci. in Mathematics, Moscow University, Dept.

                of Geometry and Topology, September 1972. Thesis:

                "Solution of multidimensional Plateau problem in

                the spectral bordism classes on Riemannian mani-



Occupation:     July 1963 - June 1967:

                   Student of Moscow Univ.,

                   Dept. of Math. and Mech. Mathematician.

                October 1967 - December 1969:

                   Post-graduate student of Moscow Univ., Dept. of

                   Math and Mech., Chair of Differential Geometry

                   and Topology.

                December 1969 - May 1974:

                   Research Fellow, Moscow Univ., Dept. of Math.

                   and Mech., Chair of Geometry and Topology.

                May 1974 - January 1980:

                   Senior research fellow, Moscow Univ., Dept. of

                   Math. and Mech. Chair of Geometry and Topology.

                January 1980 - March 1992:

                   Professor of Moscow Univ., Dept.of Math. and

                   Mech., Chair of Geometry and Topology.

                March 1992 - to present time: Chair of

                   Differential Geometry and Applications.

                   Dept. of Math. and Mech. Moscow State



Membership of Professional Societies:


                Full member of Russian Academy of Sciences


                Member of International Academy of Science of High



                Member of Academy of Natural Sciences (Russia),


                Member of Moscow Mathematical Society.


Prizes, Awards and Distinctions:


                Award of Moscow Mathematical Society, 1974.

                Award of the  Presidium  of  Academy  of  Science,

                USSR, 1987.

                State Award of Russia, 1996.


Research and Publications:

                210  publications  in  the  central   mathematical

                press. The main fields of investigations:


                1) Variational methods  in  differential  geometry

                   and topology, minimal surfaces and Plateau

                   problem, harmonic mappings.

                2) Integration of Hamiltonian systems of differen-

                   tial equations, including a new theory of topological

                   classificaion of such systems.

                3) Computer geometry, algorithmical problems in

                   geometry and topology. Computers in the topolo-

                   gy of three-dimensional manifolds.

                4) Empirico-statistical methods for the analysis

                   of narrative texts, the problem of recogniza-

                   bility of dependent texts. Applications to the

                   chronology of ancient history.


The main scientific publications:


The main books:  1)  Fomenko  A.T.  Differential  Geometry   and

                   Topology.  - Plenum Publ. Corporation.    1987.

                   Ser.Contemporary Soviet Mathematics.Consultants

                   Bureau, New York and London.(In English)

                   Translation from Russian edition.


                   2) Dubrovin B.A., Fomenko A.T., Novikov S.P.

                   Modern  Geometry.  Methods  and   Applications.

                   Springer-Verlag, GTM 93, Part 1, 1984; GTM 104,

                   Part 2, 1985.(In English), Part 3, 1990, GTM 124.

                   Translation from Russian edition.


                   3) Fomenko A.T., Trofimov V.V., Integrable

                   systems on Lie algebras and symmetric spaces.-

                   Gordon and Breach, 1987. (In English)


                   4)  Fomenko  A.T. Integrability and Noninteg-

                   rability in Geometry and Mechanics. - Kluwer

                   Academic Publishers, 1988. (In English)


                   5) Fomenko A.T., Fuchs D.B., Gutenmacher V.L.

                   Homotopic Topology. - Akademiai Kiado, Buda-

                   pest, 1986. (In English). Translation from the

                   Russian edition 1969. Japanese translation in



                   6) Fomenko A.T. Symplectic Geometry. Methods

                   and Applications. - Gordon and Breach , 1988.

                   Translation from Russian edition. Second edition

                   in 1996.


                   7) Novikov S.P., Fomenko A.T. The basic ele-

                   ments of differential geometry and topology.

                   Moscow, Nauka, 1987.  English translation,

                   Kluwer Acad. Publishers, 1990.


                   8) Dao Chong Thi, Fomenko A.T. Minimal surfaces

                   and Plateau problem. Moscow, Nauka, 1987.

                   English translation, American Math.Society,



                   9) Fomenko A.T. Topological variational prob-

                   lems. Moscow, Moscow Univ. Press.1984.  English

                   translation, Gordon and Breach, 1991.


                   10) Fomenko A.T.  Variational Principles in

                   Topology. Multidimensional Minimal Surface Theory.

                   Kluwer Acad. Publishers. 1990.


                   11) Fomenko A.T. Visual Geometry and Topology.

                   Moscow, Moscow Univ. Press, 1992. (English

                   translation, Springer-Verlag, 1994).


                   12) Fomenko A.T. The Plateau Problem. vols.1,2.

                   Gordon and Breach, 1990. (Studies in the Develop-

                   ment of Modern Mathematics).(In English)


                   13) Fomenko A.T. Mathematical Impressions. American

                   Math. Society, 1990.


                   14) Fomenko A.T., Tuzhilin A.A. Elements of the

                   Geometry of Minimal Surfaces in Three-Dimensional

                   Space. - American Math. Soc. in: Translation of

                   Mathematical Monographs. vol.93, 1991.


                   15) Fomenko A.T., Matveev S.V. Algorithmical and

                   Computer Methods in Three-Dimensional Topology.

                   - Moscow, Moscow Univ.Press, 1991.

                   English translation in Kluwer Academic Publishers,

                   The Netherlands, 1997.


                   16) Fomenko A.T. Methods for Statistical Analysis

                   of Narrative Texts and Applications to Chronology.

                   (Recognition and Dating of Dependent Texts, Statis-

                   tical Ancient Chronology, Statistics of Ancient

                   Astronomical Records). - Moscow, Moscow Univ.Press.

                   1990 (in Russian).


                   17) Fomenko A.T., Kalashnikov V.V., Nosovsky G.V.

                   Geometrical and Statistical Methods of Analysis

                   of Star Configurations. Dating of Ptolemy's

                   Almagest. - Moscow, Nauka.

                   English translation in CRC Press, USA, 1993.


                   18) A.T.Fomenko. Empirico-Statistical Analysis

                   of Narrative Material and its Applications to

                   Historical Dating. (In English).

                       Volume 1: The Development of the Statistical


                       Volume 2: The Analysis of Ancient and Medieval


                   Kluwer Academic Publishers. 1994. The Netherlands.


                   19) A.T.Fomenko. Visual Geometry and Topology.

                   Springer-Verlag. 1994. (In English).


                   20) A.T.Fomenko, V.V.Trofimov. Algebra and Geometry

                   of Integrable Hamiltonian Differential Equations. -

                   Moscow, "Factorial", 1995 (In Russian).


                   21) A.T.Fomenko, T.L.Kunii. Topological

                   Modeling for Visualization. - Springer-Verlag, 1997.



The main publications in the central mathematical journals:


1)   Fomenko A.T.  Realization  of  cycles  in  compact  symmetric

spaces by totally geodesic  submanifolds.  -  Soviet  Math.  Dokl.

V.11, 1970, No. 6, P. 1583 - 1586 (in English).


2)   Fomenko A.T. Bott periodicity rrom the point of  view  of  an

n-dimensional Dirichlet functional. - Math. USSR Izvestija, V.  5,

1971, No.3, P. 681 - 695 (in English).


3)   Fomenko A.T. Minimal compacts  in  Riemannian  manifolds  and

Reifenberg's conjecture.- Math. USSR Izvestija. V.6, 1972, No.  5,

P.1037 - 1066 (in English).


4)   Fomenko  A.T.  The  multidimensional  Plateau   problem   in

Riemannian manifolds. - Math. USSR Sbornik, V. 18, 1972, No. 3, P.

487 - 527 (in English).


5)   Fomenko A.T., Volodin I.A., Kuznetzov V.E. On the problem  of the

algorithmical  recognizability  of  the  standard three-dimensional

sphere. - Uspechi Math. Nauk, 1974, V.24, No. 5, P. 71 - 168

(in Russian, but see also corresponding English translation).


6)   Fomenko A.T.Complete  Integrability  of  some  Classical

Hamiltonian Systems. -  Amer. Math. Soc. Trans. (2), V.133,  1986,

P.79 - 9 (in English).


7)    Fomenko  A.T.  Algebraic  structure  of  certain  integrable

Hamiltonian Systems, - Lecture Notes in Math. 1984, V.1108,  P.103

- 127 (in English).


8)   Fomenko A.T. The topology of surfaces of constant  energy  in

integrable  Hamiltonian   systems,   and   the   obstructions   to

integrability. - Math. USSR Izyestija, V.29, 1987, No.3,  P.629  -

658 (in English).


9)   Fomenko A.T. Morse theory of integrable Hamiltonian  systems.

- Soviet Math. Dokl. V.33, 1986, No.2, P. 502 - 506 (in English).


10)  Fomenko  A.T.  Symplectic  Topology  of  Completely Integrable

Hamiltonian Systems. - Russian Math. Surveys. 1989. v.44, No.1, pp.

181 - 219 (in English).


11)  Fomenko  A.T.  Empirico-Statistical  Methods  in   Ordering

Narrative Texts. - International Statistical Review.  1988,  V.56,

No.3, P.279 - 301 (in English).


12)  Fomenko A.T., Matveev S.V. Constant energy surfaces of Hamilto-

nian systems, enumeration of three-dimensional manifolds in increasing

order of complexity, and computation of volumes of closed hyperbolic

manifolds. - Russian Math. Surveys, v.43, No.1, 1988, pp. 3 - 24 (in



13)  Chacon R.V., Fomenko A.T. Reccurence formula for the homogeneous

terms of the logarithm of the product integral on Lie groups. -

Functional Analisys and its Applic. 1990, v.24, No.1, pp.48-58 (in

Russian, but see also corresponding English translation).


14)  Fomenko A.T. Topological invariants of integrable Hamiltonian

systems. - Functional Analysis and its Applic. 1988, v.22, No.4, pp.

38 - 51 (in Russian, but see also corresponding English translation).


15)  Bolsinov A.V., Fomenko A.T., Matveev S.V. Topological classifi-

cation of integrable Hamiltonian systems with two degrees of freedom.

List of all systems of low complexity. - Russian Math.Surveys.

vol.45, 1990, No.2, pp.59-94.


16)  Fomenko A.T. List of all integrable Hamiltonian systems of

general type with two degress of freedom. "Physical zone" in this

table. - In: Integrable and superintegrable systems. World Scientific

Publ. Co. Ptl.Ltd. 1990, pp.134-164.


17)  Fomenko A.T. Topological classification of all Hamiltonian

differential equations of general type with two degrees of freedom.

- In: Geometry of Hamiltonian Systems. Proc. of a Workshop held

June 5-16, 1989. Berkeley. Springer Verlag. New York. 1991, pp.



18)  Fomenko A.T. A bordism theory for integrable nondegenerate

Hamiltonian systems with two degrees of freedom. A new topological

invariant of hidher-dimensional integrable systems. - Math.USSR

Izvestiya, vol.39, (1992), No.1, pp.731-759.


19)  A.V.Bolsinov, A.T.Fomenko. Orbital equivalence of

integrable Hamiltonian systems with two degrees of freedom. A

classification theorem. I,II. -

  Russian Acad. Sci. Sb. Math. 1995, vol.81, No.2,

  pp.421-465. (Part I).

  Russian Acad. Sci. Sb. Math. 1995, vol.82, No.1, pp.21-63.

  (Part II).


20)  A.V.Bolsinov and A.T.Fomenko. Orbital classification of

integrable Hamiltonian systems. The case of simple systems.

Orbital classification of systems of Euler type in rigid body

dynamics. - Izvestiya: Mathematics 59:1, (1995), pp.63-100.


21)  A.V.Bolsinov, A.T.Fomenko. Orbital classification of

geodesic flows on two-dimensional ellipsoids. The Jacobi problem

is orbitally equivalent to the integrable Euler case in rigid

body dunamics. - Functional Analysis and its Applications. 1995,

vol.29, No.3, pp.149-160.