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Andrey Yu. Konyaev

Andrey Yu. Konyaev

Candidate of Physical and Mathematical Sciences (PhD), Docent

Department of Differential Geometry and Applications
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University
Main Building, 1 Leninskiye Gory, Moscow 119991, GSP-1, Russia

E-mail: maodzund@yandex.ru

Publications (35) Full list of publications

1. Life and career

Andrey Yu. Konyaev was born in 1984 in the city of Tambov. In 1998 he entered the Tambov Regional Physics and Mathematics Lyceum (now Lyceum No. 14). During his studies he took an active part in olympiads in mathematics, physics, computer science and English; his best result was a third-degree diploma at the final round of the All-Russian Olympiad in mathematics.

In 2002, after finishing the lyceum with a gold medal, he entered the Faculty of Mechanics and Mathematics of MSU, and in 2007 graduated with honours in the specialty “Mathematics. Applied Mathematics”. His diploma thesis was “Section operators on simple complex Lie algebras and the bifurcation diagram of the moment map for the integrable systems associated with them”.

In the same year he entered the full-time postgraduate programme in specialty 01.01.04. In 2010 he completed it under the supervision of Academician A. T. Fomenko and Professor A. V. Bolsinov. His candidate dissertation “Algebraic and geometric properties of systems obtained by the shift of the argument method” was defended on 8 April 2011.

Since the autumn of 2010 he has been a member of the Department of Differential Geometry and Applications; he is now Docent at the Department and, since 2026, Head of the Laboratory of Differential Geometry of Integrable Systems.

2. Degrees and positions

Born1984, Tambov.
EducationFaculty of Mechanics and Mathematics, MSU, 2002–2007, diploma with honours; postgraduate programme 2007–2010.
Candidate of Physical and Mathematical Sciences (PhD)2011; advisors Academician A. T. Fomenko and Professor A. V. Bolsinov. Thesis: “Algebraic and geometric properties of systems obtained by the shift of the argument method”.
PositionsDepartment of Differential Geometry and Applications, MSU, since 2010; Docent. Head of the Laboratory of Differential Geometry of Integrable Systems (since 2026).
Research fieldsIntegrable Hamiltonian systems with algebraic and geometric methods; bi-Hamiltonian systems; Nijenhuis geometry; compatible Poisson structures; hydrodynamic-type systems.

3. Research

At the Department of Differential Geometry and Applications A. Yu. Konyaev studies geometric and algebraic properties of various integrable Hamiltonian systems. Of particular interest are the so-called bi-Hamiltonian systems, that is, integrable systems that are Hamiltonian with respect to a pair of compatible Poisson brackets. Many classical integrable cases belong to this class, as do the systems obtained by the shift of the argument method.

Main lines of work

  • Section operators on simple complex Lie algebras, bifurcation diagrams and discriminants of spectral curves of integrable systems on Lie algebras.
  • Completeness of commutative subalgebras associated with Nijenhuis operators, including the Sokolov–Odesskii subalgebras on gl(n).
  • Nijenhuis geometry: gl-regular Nijenhuis operators, linearization of their singularities, Frobenius pencils and compatible non-homogeneous Poisson structures, applications to multicomponent KdV, Camassa–Holm, Harry Dym and Hunter–Saxton equations.
  • Orthogonal separation of variables for spaces of constant curvature and geodesic equivalence of metrics; existence of Riemannian invariants for integrable systems of hydrodynamic type.
  • Classification of Lie algebras whose coadjoint orbits in general position are two-dimensional.

4. Teaching and seminars

A. Yu. Konyaev runs seminars on the courses of classical differential geometry and computer geometry, and is co-leader of the research seminar “Bi-Hamiltonian Structures and Integrable Systems”.

He has taken part in numerous conferences, among them the Summer School and Conference on Poisson Geometry (Trieste, Italy, 2005), the Voronezh Winter Mathematical School of S. G. Krein (2006, 2009), the Lomonosov Readings (2006) and the 5th International Conference on Differential and Functional Differential Equations (2008).

5. Publications

Full list of publications — 42 records (department page and ISTINA profile)

  1. A. V. Bolsinov, A. Yu. Konyaev, V. S. Matveev. Existence of Riemannian invariants for integrable systems of hydrodynamic type. Physica D: Nonlinear Phenomena, 495 (2026), 135304.
  2. M. M. Chernin, A. Yu. Konyaev. On operator fields in an upper triangular Toeplitz form. Russian Journal of Mathematical Physics, 33:1 (2026), pp. 42–55.
  3. E. S. Kogan, A. Yu. Konyaev. Small Nijenhuis cohomology and its properties. Matematicheskii Sbornik, 217:6 (2026), pp. 34–50.
  4. A. V. Bolsinov, A. Yu. Konyaev, V. S. Matveev. Finite-dimensional reductions and finite-gap-type solutions of multicomponent integrable PDEs. Studies in Applied Mathematics, 155:2 (2025), e70100.
  5. A. V. Bolsinov, A. Yu. Konyaev, V. S. Matveev. Integrability of the magnetic geodesic flow on the sphere with a constant 2-form. International Journal of Geometric Methods in Modern Physics (2025), 2650041.
  6. A. V. Bolsinov, A. Yu. Konyaev, V. S. Matveev. On the Jordan–Chevalley decomposition problem for operator fields in small dimensions and the Tempesta–Tondo conjecture. Journal of Geometry and Physics, 218 (2025), 105656.
  7. A. V. Bolsinov, A. Yu. Konyaev, V. S. Matveev. Applications of Nijenhuis geometry V: geodesic equivalence and finite-dimensional reductions of integrable quasilinear systems. Journal of Nonlinear Science, 34:2 (2024), 33.
  8. A. V. Bolsinov, A. Yu. Konyaev, V. S. Matveev. Nijenhuis geometry IV: conservation laws, symmetries and integration of certain non-diagonalisable systems of hydrodynamic type in quadratures. Nonlinearity, 37:10 (2024), 105003.
  9. E. I. Antonov, A. Yu. Konyaev. Nijenhuis operators with a unity and F-manifolds. Journal of the London Mathematical Society, 110:3 (2024).
  10. On the linearization of certain singularities of Nijenhuis operators. Russian Journal of Mathematical Physics, 31:1 (2024), pp. 106–111.
  11. A. V. Bolsinov, A. Yu. Konyaev, V. S. Matveev. Orthogonal separation of variables for spaces of constant curvature. Forum Mathematicum (2024).
  12. A. Yu. Konyaev, E. A. Kudryavtseva, V. I. Sidelnikov. Geometry and topology of two-dimensional symplectic manifolds with generic singularities and Hamiltonian systems on them. Moscow University Mathematics Bulletin, no. 5 (2024), pp. 22–33.
  13. A. V. Bolsinov, A. Yu. Konyaev, V. S. Matveev. Applications of Nijenhuis geometry III: Frobenius pencils and compatible non-homogeneous Poisson structures. Journal of Geometric Analysis, 33:6 (2023).
  14. A. V. Bolsinov, A. Yu. Konyaev, V. S. Matveev. Applications of Nijenhuis geometry IV: multicomponent KdV and Camassa–Holm equations. Dynamics of Partial Differential Equations, 20:1 (2023), pp. 73–98.
  15. A. V. Bolsinov, A. Yu. Konyaev, V. S. Matveev. Nijenhuis geometry III: gl-regular Nijenhuis operators. Revista Matematica Iberoamericana (2023).
  16. Symmetric matrices and maximal Nijenhuis pencils. Matematicheskii Sbornik, 214:8 (2023), pp. 53–62.
  17. A. Yu. Konyaev, J. M. Kress, V. S. Matveev. When a (1,1)-tensor generates separation of variables of a certain metric. Journal of Geometry and Physics (2023), 105031.
  18. Geometry of inhomogeneous Poisson brackets, multicomponent Harry Dym hierarchies and multicomponent Hunter–Saxton equations. Russian Journal of Mathematical Physics, 29 (2022), pp. 518–541.
  19. A. V. Bolsinov, A. Yu. Konyaev, V. S. Matveev. Applications of Nijenhuis geometry II: maximal pencils of multi-Hamiltonian structures of hydrodynamic type. Nonlinearity, 34:8 (2021), pp. 5136–5162.
  20. A. V. Bolsinov, A. Yu. Konyaev, V. S. Matveev. Applications of Nijenhuis geometry: non-degenerate singular points of Poisson–Nijenhuis structures. European Journal of Mathematics (2021).
  21. A. V. Bolsinov, A. Yu. Konyaev, V. S. Matveev. Nijenhuis geometry. Advances in Mathematics (2021), 108001.
  22. Nijenhuis geometry II: left-symmetric algebras and the linearization problem for Nijenhuis operators. Differential Geometry and its Applications, 74 (2021), 101706.
  23. Completeness of the Sokolov–Odesskii commutative subalgebras and Nijenhuis operators on gl(n). Matematicheskii Sbornik, 211:4 (2020), pp. 583–593.
  24. G. I. Sharygin, A. Yu. Konyaev. Survey of the deformation quantization of commutative families. In: Recent Developments in Integrable Systems and Related Topics of Mathematical Physics, Springer Proceedings in Mathematics & Statistics, 273 (2018).
  25. Completeness of some commutative subalgebras associated with Nijenhuis operators on Lie algebras. Doklady Mathematics, 479:3 (2018), pp. 247–249.
  26. A. T. Fomenko, A. Yu. Konyaev. Geometry, dynamics and different types of orbits. Journal of Fixed Point Theory and its Applications, 15:49 (2015), pp. 49–66.
  27. A. T. Fomenko, A. Yu. Konyaev. Algebra and geometry through Hamiltonian systems. Continuous and Distributed Systems, 211 (2014), pp. 3–21.
  28. Classification of Lie algebras with coadjoint orbits of general position of dimension 2. Matematicheskii Sbornik, 205:1 (2014), pp. 47–66.
  29. A. T. Fomenko, A. Yu. Konyaev. New approach to symmetries and singularities in integrable Hamiltonian systems. Topology and its Applications, 159:7 (2012), pp. 1964–1975.
  30. A. V. Bolsinov, A. M. Izosimov, A. Yu. Konyaev, A. A. Oshemkov. Algebra and topology of integrable systems. Research problems. Proceedings of the Seminar on Vector and Tensor Analysis, 28 (2012), pp. 119–191.
  31. A. V. Bolsinov, A. Yu. Konyaev. Algebraic and geometric properties of quadratic Hamiltonians defined by section operators. Mathematical Notes, 90:5 (2011), pp. 689–702.
  32. Uniqueness of the reconstruction of the parameters of section operators on simple complex Lie algebras. Mathematical Notes, 90:3 (2011), pp. 384–393.
  33. The bifurcation diagram and the discriminant of the spectral curve of integrable systems on Lie algebras. Matematicheskii Sbornik, 201:9 (2010), pp. 27–60.
  34. The bifurcation diagram and the discriminant of integrable systems of rigid body type on the Lie algebras so(2n+1), sp(2n) and sl(n). Doklady Mathematics, 421:1 (2008), pp. 18–20.
  35. Bending of plane curves by flows of an incompressible fluid. Moscow University Mathematics Bulletin, no. 5 (2006), pp. 55–57.