Anatoly Timofeevich Fomenko

1. Life and career

Anatoly Timofeevich Fomenko is a Russian mathematician, Full Member of the Russian Academy of Sciences and, since 1992, Head of the Department of Differential Geometry and Applications at the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University. He is a specialist in multidimensional calculus of variations, minimal surfaces, differential geometry and topology, the theory of Lie groups and Lie algebras, symplectic and computer geometry, Hamiltonian dynamical systems and the topology of three-dimensional manifolds.

Fomenko joined Moscow State University in 1969 as a member of the Department of Differential Geometry. He was a professor of that department from 1981 to 1983 and then professor of the Department of Higher Geometry and Topology from 1983 to 1992, when he became head of the newly created Department of Differential Geometry and Applications. He received his candidate degree in 1970, his doctoral degree in 1972 and was appointed professor in 1981; he was elected a corresponding member of the USSR Academy of Sciences in 1990 and a full member of the Russian Academy of Sciences in 1994.

His research has shaped the topology of integrable Hamiltonian systems and the theory of multidimensional minimal surfaces. In the theory of minimal surfaces he solved the multidimensional Plateau problem in the class of spectral bordisms of Riemannian manifolds. He created a new research direction: the topological classification of non-degenerate integrable Hamiltonian differential equations (dynamical systems) of general type. He discovered invariants describing the topological type of their singularities and obtained a classification of integrable Hamiltonian systems with two degrees of freedom. The development of these and related directions led to the creation of the Department of Differential Geometry and Applications at the Faculty of Mechanics and Mathematics in 1992; Fomenko has headed it since then.

At the faculty he has taught the compulsory course “Differential Geometry and Topology” for about 25 years and has created several fundamental special courses. He leads the research seminar “Modern Geometric Methods”, founded by him in 1972. By 2024, 61 candidate’s and 11 doctoral dissertations had been defended under his supervision.

2. Degrees and positions

Career: staff member of the Department of Differential Geometry, MSU (1969–1981); professor of the Department of Differential Geometry (1981–1983); professor of the Department of Higher Geometry and Topology (1983–1992); head of the Department of Differential Geometry and Applications (1992–present). He has worked at Moscow State University since 1969.

3. Research

A. T. Fomenko is known in Russia and abroad as a specialist in multidimensional calculus of variations, differential geometry and topology, the theory of Lie groups and Lie algebras, symplectic and computer geometry, and the theory of Hamiltonian dynamical systems.

Minimal surfaces and the Plateau problem

In the theory of minimal surfaces he solved the multidimensional Plateau problem in the class of spectral bordisms of Riemannian manifolds (doctoral dissertation, 1972). His monographs Variational Principles in Topology, Variational Problems in Topology and The Plateau Problem, together with Minimal Surfaces, Stratified Multivarifolds, and the Plateau Problem (with Dao Chong Thi), give a systematic account of multidimensional variational theory, minimal surface theory and the Plateau problem. Related work concerns harmonic maps, the geometry of soap films and topological variational problems.

Integrable Hamiltonian systems

Fomenko created the theory of topological classification of non-degenerate integrable Hamiltonian systems of general type. Invariants describing the topological type of singularities of such systems were discovered, and a classification of integrable Hamiltonian systems with two degrees of freedom was obtained. His work in this area includes Morse theory of integrable systems, the topology of constant-energy surfaces, obstructions to integrability, bifurcations of Liouville tori, topological billiards and the geometry of integrable geodesic flows. It is presented in the monographs Symplectic Geometry, Integrability and Nonintegrability in Geometry and Mechanics, and the two-volume Integrable Hamiltonian Systems: Geometry, Topology, Classification (with A. V. Bolsinov).

Computer geometry and three-dimensional topology

His work in computer geometry and algorithmic topology includes methods for enumerating three-dimensional manifolds in order of increasing complexity, the computation of volumes of closed hyperbolic manifolds, round Morse functions and isoenergy surfaces, and computer methods in the topology of three-manifolds. These results are reflected in the monographs Algorithmic and Computer Methods for Three-Manifolds (with S. V. Matveev) and Topological Modeling for Visualization (with T. L. Kunii), and in textbooks on computer geometry.

Mathematical methods in chronology

Fomenko has also developed empirical-statistical methods for recognizing dependent and independent narrative and historical texts and for dating historical sources. This work led to the “New Chronology” hypothesis, which has been the subject of extensive discussion in the academic community. His books in this area include Empirico-Statistical Analysis of Narrative Material and Its Applications to Historical Dating (Kluwer, 1994) and New Methods of Statistical Analysis of Historical Texts: Applications to Chronology (Edwin Mellen Press, 1999).

Main research directions

• Variational methods in differential geometry and topology; the theory of minimal surfaces and the Plateau problem; harmonic maps.
• Integration of Hamiltonian systems of differential equations; topological classification of integrable systems; the theory of invariants; Hamiltonian mechanics and symplectic geometry.
• Computer geometry; algorithmic problems in geometry and topology; computers in the topology of three-dimensional manifolds.
• Empirical-statistical methods in the problem of recognizing dependent and independent narrative and historical texts.

4. Teaching

A. T. Fomenko has taught the compulsory course “Differential Geometry and Topology” at the Faculty of Mechanics and Mathematics for about 25 years. He has created several fundamental special courses, including “Riemannian and Symplectic Geometry” and “Topology of Dynamical Systems”, and leads the research seminar “Modern Geometric Methods”, which he founded in 1972.

Courses taught over the years

• Differential Geometry and Topology
• Classical Differential Geometry
• Algorithmic and Computer Methods in Three-Dimensional Topology
• Geometry and Topology of Integrable Hamiltonian Systems
• Homotopy Topology
• Integrable Hamiltonian Systems on Lie Algebras
• Minimal Surfaces and the Plateau Problem
• Multidimensional Minimal Surfaces and Harmonic Maps
• Topological Variational Problems
• Elements of Topology and Symplectic Geometry
• Riemannian Geometry
• Visual Geometry and Topology

Recent courses (ISTINA)

• Geometry and Topology of Hamiltonian Systems (2024–2025)
• Introduction to Topology and Symplectic Geometry (2023–2024)
• Geometry and Topology in Nature and Art (2015, with A. A. Oshemkov and A. Yu. Konyaev)
• Visual Geometry and Topology (2012, with A. A. Oshemkov, A. A. Tuzhilin and A. I. Shafarevich)
• Classical Differential Geometry; Differential Geometry and Topology; Computer Geometry Practicum (2010)
• The P. K. Rashevsky Seminar (2009, with V. O. Manturov and D. P. Ilyutko)

5. Doctoral students

By 2024, 61 candidate’s dissertations and 11 doctoral dissertations had been defended under the supervision of A. T. Fomenko, all in the specialty “Geometry and Topology”. The list on the department page continues with dissertations defended in 2025. He also served as scientific consultant for several doctoral dissertations.

Among his students and doctoral graduates are Dao Chong Thi (Vietnam), V. V. Trofimov, A. V. Bolsinov, A. O. Ivanov, A. A. Tuzhilin, A. A. Oshemkov, V. V. Vedyushkina and V. A. Kibkalo. He was scientific consultant for the doctoral dissertations of S. V. Matveev, V. V. Sharko and V. V. Vedyushkina.

A list of some publications by his students in 2008–2013 is given in the departmental bibliography.

Examples of supervised topics

• Minimal surfaces and minimal flows in Riemannian manifolds; calibrations and the geometry of minimal surfaces.
• Complete integrability of Euler equations on finite-dimensional Lie algebras; integrable Hamiltonian systems on Lie algebras and symmetric spaces.
• Topological classification of Hamiltonians in classical integrable cases; invariants of integrable Hamiltonian systems; bifurcations of Liouville tori.
• Topology and classification of Liouville foliations of integrable billiards and their perturbations (2025).

6. Awards and service

Awards and honours

• 1974 — Prize of the Moscow Mathematical Society.
• 1987 — Prize in Mathematics of the Presidium of the USSR Academy of Sciences.
• 1996 — State Prize of the Russian Federation (jointly with A. S. Mishchenko) for the cycle of works “Study of invariants of smooth manifolds and Hamiltonian dynamical systems”.
• 1999 — Honoured Professor of Moscow University.
• 2009 — Full Member of the International Academy of Technological Sciences of the Russian Federation.
• 2024 — Medal of the Order “For Merit to the Fatherland”, II degree.
• 2024 — Jubilee Medal “300 Years of the Russian Academy of Sciences”.
• 2024 — Lomonosov Prize of Moscow State University for outstanding achievements in teaching.
• 2025 — Lomonosov Prize of Moscow State University for outstanding achievements in research.

Editorial boards

• Deputy Editor-in-Chief, Vestnik Moskovskogo Universiteta, Series 1: Mathematics, Mechanics.
• Member of the editorial board, Matematicheskii Sbornik.
• Member of the editorial board, Central European Journal of Mathematics.
• Editor-in-Chief of the English book series Reviews in Mathematics and Mathematical Physics (Cambridge Scientific Publishers).

Scientific community

• Member of the Academic Council of the Faculty of Mechanics and Mathematics and of the Academic Council of Moscow State University.
• Member of the expert council in mathematics at the Faculty of Mechanics and Mathematics and of the expert council of the Steklov Mathematical Institute of the Russian Academy of Sciences.
• Head of the Mathematics Division of the Faculty of Mechanics and Mathematics.
• In previous years: member of the Presidium of the Higher Attestation Commission (VAK) of the Russian Federation; deputy academic secretary of the Mathematics Division of the Russian Academy of Sciences; member of various commissions for awarding mathematical prizes of the Russian Academy of Sciences.
• Member of dissertation councils in geometry and topology.

7. Books

Mathematics and geometry

1. D. B. Fuchs, A. T. Fomenko, V. L. Gutenmacher. Homotopic Topology. Budapest: Akademiai Kiado, 1986.
2. D. B. Fuchs, A. T. Fomenko. Homotopical Topology. 2nd edition. Graduate Texts in Mathematics 273. Springer, 2016.
3. B. A. Dubrovin, A. T. Fomenko, S. P. Novikov. Modern Geometry — Methods and Applications. Part I. Graduate Texts in Mathematics 93. Springer, 1984.
4. B. A. Dubrovin, A. T. Fomenko, S. P. Novikov. Modern Geometry — Methods and Applications. Part II. Graduate Texts in Mathematics 104. Springer, 1985.
5. B. A. Dubrovin, A. T. Fomenko, S. P. Novikov. Modern Geometry — Methods and Applications. Part III: Introduction to Homology Theory. Graduate Texts in Mathematics 124. Springer, 1990.
6. A. S. Mishchenko, A. T. Fomenko. A Course of Differential Geometry and Topology. Moscow: Mir, 1988.
7. A. S. Mishchenko, Yu. P. Solovyev, A. T. Fomenko. Problems in Differential Geometry and Topology. Moscow: Mir, 1985.
8. A. T. Fomenko. Differential Geometry and Topology. New York: Plenum, 1987.
9. A. T. Fomenko. Variational Principles in Topology: Multidimensional Minimal Surface Theory. Dordrecht: Kluwer, 1990.
10. A. T. Fomenko. Variational Problems in Topology: The Geometry of Length, Area and Volume. Gordon and Breach, 1990.
11. A. T. Fomenko. The Plateau Problem. Vols. 1–2. Gordon and Breach, 1990.
12. A. T. Fomenko. Symplectic Geometry: Methods and Applications. Gordon and Breach, 1988; 2nd edition, 1995.
13. A. T. Fomenko. Integrability and Nonintegrability in Geometry and Mechanics. Dordrecht: Kluwer, 1988.
14. A. T. Fomenko, V. V. Trofimov. Integrable Systems on Lie Algebras and Symmetric Spaces. Gordon and Breach, 1987.
15. S. P. Novikov, A. T. Fomenko. Basic Elements of Differential Geometry and Topology. Dordrecht: Kluwer, 1990.
16. A. T. Fomenko, A. A. Tuzhilin. Elements of the Geometry of Minimal Surfaces in Three-Dimensional Space. Translations of Mathematical Monographs 93. American Mathematical Society, 1991.
17. Dao Chong Thi, A. T. Fomenko. Minimal Surfaces, Stratified Multivarifolds, and the Plateau Problem. Translations of Mathematical Monographs 84. American Mathematical Society, 1991.
18. A. T. Fomenko (editor). Topological Classification of Integrable Systems. American Mathematical Society, 1991.
19. A. T. Fomenko. Mathematical Impressions. Providence, RI: American Mathematical Society, 1990.
20. A. T. Fomenko. Visual Geometry and Topology. Berlin: Springer, 1994.
21. A. T. Fomenko, S. V. Matveev. Algorithmic and Computer Methods for Three-Manifolds. Dordrecht: Kluwer, 1997.
22. A. T. Fomenko, T. L. Kunii. Topological Modeling for Visualization. Berlin: Springer, 1997.
23. A. T. Fomenko, O. V. Manturov, V. V. Trofimov. Tensor and Vector Analysis: Geometry, Mechanics and Physics. Gordon and Breach, 1998.
24. A. V. Bolsinov, A. T. Fomenko. Integrable Geodesic Flows on Two-Dimensional Surfaces. New York: Kluwer Academic/Plenum, 2000.
25. A. V. Bolsinov, A. T. Fomenko. Integrable Hamiltonian Systems: Geometry, Topology, Classification. Boca Raton: Chapman & Hall/CRC, 2004.
26. A. V. Bolsinov, A. T. Fomenko, A. A. Oshemkov. Topological Methods in the Theory of Integrable Hamiltonian Systems. Cambridge Scientific Publishers, 2006.
27. A. T. Fomenko, A. S. Mishchenko, Yu. P. Solovyev. Selected Problems in Differential Geometry and Topology. Cambridge Scientific Publishers, 2013.

Mathematical chronology

1. A. T. Fomenko. Empirico-Statistical Analysis of Narrative Material and Its Applications to Historical Dating. Vol. 1: The Development of the Statistical Tools; Vol. 2: The Analysis of Ancient and Medieval Records. Dordrecht: Kluwer, 1994.
2. A. T. Fomenko. New Methods of Statistical Analysis of Historical Texts: Applications to Chronology. Vols. 1–3. Lewiston, NY: Edwin Mellen Press, 1999.

8. Selected publications

1. Bott periodicity from the point of view of n-dimensional Dirichlet functional. Mathematics of the USSR — Izvestiya 5(3), 681–695 (1971).
2. Minimal compacta in Riemannian manifolds and Reifenberg’s conjecture. Mathematics of the USSR — Izvestiya 6(5), 1037–1066 (1972).
3. The multidimensional Plateau problem in Riemannian manifolds. Mathematics of the USSR — Sbornik 18(3), 487–527 (1972).
4. A. S. Mishchenko, A. T. Fomenko. Euler equations on finite-dimensional Lie groups. Mathematics of the USSR — Izvestiya 12(2), 371–389 (1978).
5. A universal lower bound on the rate of growth of globally minimal solutions. Soviet Mathematics Doklady 21(2), 441–445 (1980).
6. Multi-dimensional variational methods in the topology of extremals. Russian Mathematical Surveys 36(6), 127–165 (1981).
7. V. V. Trofimov, A. T. Fomenko. Liouville integrability of Hamiltonian systems on Lie algebras. Russian Mathematical Surveys 39(2), 1–67 (1984).
8. Symmetries of soap films. Computers & Mathematics with Applications 12B(3/4), 825–834 (1986).
9. V. V. Fedorov, A. T. Fomenko. Statistical estimation of chronological nearness of historical texts. Journal of Soviet Mathematics 32(6), 668–675 (1986).
10. Morse theory of integrable Hamiltonian systems. Soviet Mathematics Doklady 33(2), 502–506 (1986).
11. The topology of surfaces of constant energy in integrable Hamiltonian systems, and obstructions to integrability. Mathematics of the USSR — Izvestiya 29(3), 629–658 (1987).
12. A. T. Fomenko, H. Zieschang. On the topology of the three-dimensional manifolds arising in Hamiltonian mechanics. Soviet Mathematics Doklady 35(2), 520–534 (1987).
13. Qualitative geometrical theory of integrable systems. Classification of isoenergetic surfaces and bifurcation of Liouville tori at the critical values. Lecture Notes in Mathematics 1334, 221–245 (1988).
14. A. T. Fomenko, H. Zieschang. On typical topological properties of integrable Hamiltonian systems. Mathematics of the USSR — Izvestiya 32(2), 385–412 (1989).
15. S. V. Matveev, A. T. Fomenko, V. V. Sharko. Round Morse functions and isoenergy surfaces of integrable Hamiltonian systems. Mathematics of the USSR — Sbornik 63(2), 319–336 (1989).
16. A. T. Fomenko, A. Yu. Konyaev. New approach to symmetries and singularities in integrable Hamiltonian systems. Topology and its Applications 159, 1964–1975 (2012).
17. E. A. Kudryavtseva, A. T. Fomenko. Each finite group is a symmetry group of some map (an “atom”-bifurcation). Moscow University Mathematics Bulletin 68(3), 148–155 (2013).
18. V. V. Vedyushkina, A. T. Fomenko. Integrable topological billiards and equivalent dynamical systems. Izvestiya: Mathematics 81(4), 688–733 (2017).

Full list of publications — 545 records (department page and ISTINA profile)

9. Citations

Citation data as of November 2024, according to different bibliographic databases (as given on the department page).

Math-Net.Ru also reports 349 research articles and 123 cited articles, with 3,083 links in Math-Net.Ru, 1,183 in Web of Science and 1,728 in Scopus.

10. Autobiography

His autobiography, Every History Wants to Be Told. My Path: Donetsk, Magadan, Lugansk, Moscow, was published in Moscow by AST in 2017 in the series How It Really Was; an expanded version appeared in 2021. The book includes fragments of the memoirs of his father Timofey Grigorievich Fomenko (1910–1992), At the Foot, and of his mother Valentina Polikarpovna Fomenko (née Markova, 1918–2009), together with his own recollections, the history of the family, and appendices on the VEAF-TOPAZ music club of the Faculty of Mechanics and Mathematics and on the RAS Commission on Pseudoscience.

The full Russian text, including the table of contents and the chapters on his parents, is available on the department page.

11. Links and sources

• Russian personal page at the Department of Differential Geometry and Applications: dfgm.math.msu.su/people/fomenko/ (full biography, research interests, books, lists of publications, students, citations and the autobiography).
• Page in the Chronicle of Moscow University (Letopis): English translation; Russian original.
• ISTINA profile: IRID 1089091; MathSciNet MR Author ID 190963; Scopus Author ID 16405920200.

This English page was compiled from the department page at dfgm.math.msu.su/people/fomenko/ (biography, research interests, teaching, books, supervised dissertations, citations and autobiography) and from the ISTINA profile (degrees, positions, awards, editorial boards and courses). Bibliographic details were checked on 11 November 2026.