Viktoria V. Vedyushkina

1. Life and career

Viktoria V. Vedyushkina was born in 1990 in the city of Volgodonsk, Rostov Region. In 2007 she finished the Classical Lyceum No. 1 at Rostov State University with a gold medal and entered the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University, graduating in 2012 with honours.

In 2012–2015 she studied in the postgraduate programme of the Division of Mathematics of the Faculty under the supervision of Academician A. T. Fomenko, and in 2016 defended her candidate dissertation “Topological classification of integrable billiards”. During her postgraduate studies she taught the computer practicum for students. In December 2016 she was appointed assistant at the Department of Differential Geometry and Applications.

In 2020 she defended her doctoral dissertation “Integrable billiards on cell complexes and integrable Hamiltonian systems” and since 2020 has been Professor at the Department.

She is a laureate of the Moscow Government Prize for young scientists (2019), of the Gold Medal of the Russian Academy of Sciences for young scientists (2020) and of the Shuvalov Prize of MSU (2021). Twice (in 2020 and 2022) she received the scholarship of Moscow State University for young staff members, postgraduate and undergraduate students who have achieved significant results in teaching and research. In 2025 she became a laureate of the Presidential Prize of the Russian Federation for young scientists.

Together with A. T. Fomenko and V. A. Kibkalo she leads the “billiard group”, students and postgraduate students developing the theory of integrable billiards.

2. Degrees and positions

3. Research

Many works have been devoted to the mathematical billiard, that is, the motion of a material point in a plane domain bounded by a piecewise smooth curve with absolutely elastic reflection at the boundary. One of the classical questions concerns the existence of periodic trajectories and the integrability of the billiard depending on its boundary. For instance, every triangle possesses a three-link periodic billiard trajectory, namely the triangle of least perimeter with vertices at the feet of the altitudes (Fagnano's theorem). Today, plane billiards bounded by arcs of confocal quadrics are a popular class of integrable billiards.

The integrability of the billiard in a domain bounded by an ellipse was noticed by G. D. Birkhoff; the integrability of the geodesic flow on an ellipsoid follows from the Jacobi–Chasles theorem. Integrability is preserved on passing to plane domains bounded by arcs of ellipses and hyperbolas of one confocal family without corner points with angles of 270 degrees. V. V. Kozlov and D. V. Treshchev observed that these systems are completely Liouville integrable and that their integrability is equivalent to the small Poncelet theorem; up to Liouville equivalence such systems were studied by V. Dragovich, M. Radnovich and V. V. Vedyushkina.

V. V. Vedyushkina classified all locally plane billiards bounded by arcs of confocal ellipses and hyperbolas (not necessarily isometrically embeddable in the plane), as well as domains, not necessarily plane, obtained by gluing elementary domains along convex boundary segments. She then studied the topology of Liouville foliations on the isoenergetic surfaces of such billiards, computing the marked Fomenko–Zieschang molecules, the invariants of Liouville equivalence.

Analysing a large number of marked molecules computed for various billiards and other integrable systems with two degrees of freedom, A. T. Fomenko formulated the conjecture that many sufficiently complicated cases of integrability are billiard-equivalent, that is, Liouville equivalent to some billiard. Together with Fomenko she developed the theory of topological billiards and billiard books, proved that billiard books realize all bases of Liouville foliations of integrable Hamiltonian systems, and obtained topological obstructions to the realizability of integrable systems by billiards. Further work concerned evolutional force billiards, billiards with slipping, billiards in magnetic fields, and the realizability of numerical invariants.

4. Teaching and supervision

Since her postgraduate years V. V. Vedyushkina has taught the computer practicum and courses of the Department. Together with A. T. Fomenko and V. A. Kibkalo she supervises the “billiard group” of students and postgraduate students working on the theory of integrable billiards.

5. Publications (selected)

Full list of publications — 131 records (department page and ISTINA profile)

1. V. V. Vedyushkina. Topological classification of integrable billiards. Candidate dissertation, Moscow, MSU, 2016.
2. V. V. Vedyushkina, A. T. Fomenko, A. O. Ivanov, A. A. Tuzhilin. Integrable billiards and their applications in geometry and dynamics. Intelligent Systems. Theory and Applications, vol. 21, no. 2 (2017).
3. V. V. Vedyushkina, A. T. Fomenko. Integrable topological billiards and equivalent dynamical systems. Izvestiya: Mathematics, vol. 81, no. 4 (2017), pp. 20–67.
4. Liouville foliation of non-convex topological billiards. Doklady Akademii Nauk, vol. 478, no. 1 (2018), pp. 7–11.
5. Fomenko–Zieschang invariants of topological billiards bounded by confocal parabolas. Moscow University Mathematics Bulletin, no. 4 (2018), pp. 22–28.
6. V. V. Vedyushkina, I. S. Kharcheva. Billiard books model all three-dimensional bifurcations of integrable Hamiltonian systems. Matematicheskii Sbornik, vol. 209, no. 12 (2018).
7. V. V. Vedyushkina, A. T. Fomenko. Topological obstructions to the realizability of integrable Hamiltonian systems by billiards. Doklady Akademii Nauk, vol. 488, no. 5 (2019), pp. 103–107.
8. V. V. Vedyushkina, A. T. Fomenko. Billiards and integrability in geometry and physics: a new view and new possibilities. Moscow University Mathematics Bulletin, no. 3 (2019), pp. 15–25.
9. V. V. Vedyushkina, A. T. Fomenko. Lowering the degree of integrals of Hamiltonian systems with the help of billiards. Doklady Akademii Nauk, vol. 486, no. 2 (2019), pp. 151–155.
10. V. V. Vedyushkina, A. T. Fomenko. Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards. Izvestiya: Mathematics, vol. 83, no. 6 (2019), pp. 63–103.
11. Fomenko–Zieschang invariants of non-convex topological billiards. Matematicheskii Sbornik, vol. 210, no. 3 (2019), pp. 17–74.
12. A. T. Fomenko, V. V. Vedyushkina. Topological billiards, conservation laws and classification of trajectories. In: Functional Analysis and Geometry: Selim Grigorievich Krein Centennial, Contemporary Mathematics, vol. 733, AMS, 2019, pp. 129–148.
13. V. V. Vedyushkina, V. A. Kibkalo, A. T. Fomenko. Topological modelling of integrable systems by billiards: realization of numerical invariants. Doklady Mathematics, vol. 493, no. 1 (2020), pp. 9–12.
14. Liouville foliation of a billiard book modelling the Goryachev–Chaplygin case. Moscow University Mathematics Bulletin, no. 1 (2020), pp. 64–68.
15. V. V. Vedyushkina, V. A. Kibkalo. Billiard realization of the numerical invariant of the Seifert fibration of integrable systems. Moscow University Mathematics Bulletin, no. 4 (2020), pp. 22–28.
16. Integrable billiards realize toric foliations on lens spaces and the 3-torus. Matematicheskii Sbornik, vol. 211, no. 2 (2020), pp. 46–73.
17. Trajectory invariants of plane billiards bounded by arcs of confocal quadrics and containing foci. Moscow University Mathematics Bulletin, no. 4 (2021), pp. 48–51.
18. Topological type of isoenergetic surfaces of billiard books. Matematicheskii Sbornik, vol. 212, no. 12 (2021), pp. 3–19.
19. V. V. Vedyushkina, A. T. Fomenko. Force evolutional billiards and the billiard equivalence of the Euler and Lagrange cases. Doklady Akademii Nauk, vol. 496 (2021), pp. 5–9.
20. V. V. Vedyushkina, V. A. Kibkalo, S. E. Pustovoitov. Realization of focus singularities of integrable systems by billiard books with Hooke potential. Chebyshevskii Sbornik, vol. 22, no. 5 (2021), pp. 2–15.
21. Local modelling of Liouville foliations by billiards: realization of edge invariants. Moscow University Mathematics Bulletin, no. 2 (2021), pp. 28–32.
22. V. V. Vedyushkina, I. S. Kharcheva. Billiard books realize all bases of Liouville foliations of integrable Hamiltonian systems. Matematicheskii Sbornik, vol. 212, no. 8 (2021), pp. 89–150.
23. A. T. Fomenko, V. V. Vedyushkina, V. N. Zavyalov. Liouville foliations of topological billiards with slipping. Russian Journal of Mathematical Physics, vol. 28 (2021), pp. 37–55.
24. A. T. Fomenko, V. V. Vedyushkina. Evolutional force billiards. Izvestiya: Mathematics, vol. 86, no. 5 (2022), pp. 114–154.
25. V. V. Vedyushkina, A. I. Skvortsov. Topology of an integrable billiard in an ellipse on the Minkowski plane with Hooke potential. Moscow University Mathematics Bulletin, no. 1 (2022), pp. 8–19.
26. V. V. Vedyushkina, V. N. Zavyalov. Realization of geodesic flows with a linear integral by geodesic billiards. Matematicheskii Sbornik, vol. 213, no. 12 (2022), pp. 3–24.
27. V. V. Vedyushkina, V. A. Kibkalo. Billiard books of small complexity and the realization of Liouville foliations of integrable systems. Chebyshevskii Sbornik, vol. 23, no. 1 (2022), pp. 53–82.
28. V. V. Vedyushkina, S. E. Pustovoitov. Classification of Liouville foliations of integrable topological billiards in a magnetic field. Matematicheskii Sbornik, vol. 214, no. 2 (2023), pp. 23–57.

Doctoral dissertation: “Integrable billiards on cell complexes and integrable Hamiltonian systems” (2020). The full list of publications (131 records) is given on the Full list of publications page.

6. Links and sources

• Russian personal page: dfgm.math.msu.su/people/vedushkina/.
• ISTINA profile: istina.msu.ru.

Compiled from the department page dfgm.math.msu.su/people/vedushkina/. Titles of Russian-language papers are translated into English; names and journal titles are transliterated.