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Gleb V. Belozerov

Gleb V. Belozerov

Staff member of the Department of Differential Geometry and Applications

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: belozerov.gleb@math.msu.ru

Full list of publications Publications (13)

1. Life and career

Gleb V. Belozerov was born on 16 January 1998 in the village of Yurginskoye, Tyumen Region. In 2016 he graduated with a gold medal from the Yurginskoye secondary school and entered the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University.

In 2022 he graduated with honours. Under the supervision of Academician Anatoly T. Fomenko he defended his diploma thesis “Topology of Liouville foliations of integrable billiards on three-dimensional tables bounded by confocal quadrics”. In the autumn of 2022 he entered the full-time postgraduate programme in specialty 1.1.3 (Geometry and Topology).

Since February 2023 he has been a staff member of the Department of Differential Geometry and Applications. In 2025 he became a laureate of the Presidential Prize of the Russian Federation for young scientists.

2. Degrees and positions

Born16 January 1998, Yurginskoye, Tyumen Region.
EducationFaculty of Mechanics and Mathematics, MSU, 2016–2022; diploma with honours (2022).
Postgraduate studyFull-time postgraduate programme, specialty 1.1.3 “Geometry and Topology”, since autumn 2022.
PositionStaff member of the Department of Differential Geometry and Applications since February 2023.
AwardsLaureate of the Presidential Prize of the Russian Federation for young scientists (2025).
Research fieldsTopology of Liouville foliations of integrable billiards (mainly three-dimensional) and of the smooth systems associated with them; billiards bounded by confocal quadrics; relations with planar billiards.

3. Research

At the Department G. V. Belozerov studies the topology of Liouville foliations of integrable billiards, mainly three-dimensional ones, and of closely related smooth systems.

Describing the topology of the Liouville foliation of an arbitrary integrable system with three degrees of freedom is a difficult problem, since no convenient machinery for such systems is available at present. For billiards bounded by confocal quadrics, however, the problem becomes tractable: such billiards possess visual first integrals, namely the parameters of the caustics.

In the study of three-dimensional billiards a close connection with planar billiards, which are actively studied at the Department, is observed. His results include a topological classification of integrable geodesic billiards in three-dimensional Euclidean space, a classification of billiards bounded by confocal quadrics, the topology of isoenergetic 5-surfaces of a billiard inside a triaxial ellipsoid with Hooke potential, integrability of the geodesic flow on the intersection of several confocal quadrics in Rn, and trajectory invariants of billiards (with A. T. Fomenko).

4. Publications

Full list of publications — 59 records (department page and ISTINA profile)

  1. Topological classification of integrable geodesic billiards in three-dimensional Euclidean space. Matematicheskii Sbornik, vol. 211, no. 11 (2020), pp. 3–40.
  2. Topological classification of billiards in three-dimensional Euclidean space bounded by confocal quadrics. Matematicheskii Sbornik, vol. 213, no. 2 (2022), pp. 3–36.
  3. Topology of isoenergetic 5-surfaces of a three-dimensional billiard inside a triaxial ellipsoid with Hooke potential. Moscow University Mathematics Bulletin, vol. 77, no. 6 (2022), pp. 21–31.
  4. Integrability of the geodesic flow on the intersection of several confocal quadrics. Doklady Mathematics, vol. 509 (2023), pp. 5–7.
  5. The geodesic flow on the intersection of several confocal quadrics in Rn. Matematicheskii Sbornik, vol. 214, no. 7 (2023), pp. 3–26.
  6. G. V. Belozerov, A. T. Fomenko. Trajectory invariants of billiards and linearly integrable geodesic flows. Matematicheskii Sbornik, vol. 215, no. 5 (2024), pp. 3–46.
  7. G. V. Belozerov, A. T. Fomenko. Rotation functions of integrable billiards as trajectory invariants. Doklady Mathematics, vol. 515 (2024), pp. 1–5.
  8. G. V. Belozerov, A. T. Fomenko. The generalized Jacobi–Chasles theorem in non-Euclidean spaces. Matematicheskii Sbornik, vol. 215, no. 9 (2024), pp. 30–55.
  9. A. T. Fomenko, G. V. Belozerov. Hidden symmetries in Hamiltonian geometry, topology, physics and mechanics. Priroda, no. 1 (2025), pp. 23–29.
  10. G. V. Belozerov, A. T. Fomenko. Trajectory invariants of non-compact integrable systems with two degrees of freedom. Moscow University Mathematics Bulletin, no. 2 (2025), pp. 79–83.
  11. G. V. Belozerov, V. N. Zavyalov. Topology of Liouville foliations of three-dimensional billiards with slipping. Chebyshevskii Sbornik, vol. 26, no. 2 (2025).
  12. Non-degenerate singularities of a three-dimensional billiard bounded by an ellipsoid in a Hooke potential field. Lobachevskii Journal of Mathematics, vol. 46, no. 3 (2025), pp. 983–1000.
  13. G. Belozerov, A. Fomenko. Singularities of three-dimensional billiards bounded by confocal quadrics. Theoretical and Applied Mechanics, vol. 52, no. 2 (2025).