Language: Russian | English
Denis P. Ilyutko

Denis P. Ilyutko

Candidate of Physical and Mathematical Sciences (PhD), Assistant Professor

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: ilyutko@yandex.ru

Publications Full list of publications

1. Life and career

Denis P. Ilyutko was born on 29 July 1979 in Krasnogorsk, Moscow Region. In 1986 he entered the basketball class of Secondary School No. 4 in Krasnogorsk, and in 1993 transferred to the physics and mathematics class of the same school, which he finished in 1996. In 1996 he took first and second places at the district and regional olympiads in physics and mathematics respectively.

After school he entered the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University, graduating in 2001 with honours in the specialty “Mathematics. Applied Mathematics”. In 2001 he entered the full-time postgraduate programme of the Faculty in specialty 01.01.04 and in 2004 completed it at the Department of Differential Geometry and Applications under the supervision of Professor A. A. Tuzhilin. In 2005 he defended his candidate dissertation “Geometry of locally minimal and extremal networks in normed spaces” (specialty 01.01.04).

Since 2003 D. P. Ilyutko has worked at the Faculty of Mechanics and Mathematics as assistant professor of the Department of Differential Geometry and Applications.

At school he played basketball actively: he was a repeated champion and prize-winner of basketball competitions among the sports schools of Moscow Region and took part in intercity basketball competitions in Leningrad and in Gorlovka (Donetsk Region, Ukraine). As a student he played handball for the Faculty team. Since 1998 he has been a member of the military hunting society and has taken part in clay-pigeon shooting competitions among military hunters' teams.

2. Degrees and positions

Born29 July 1979, Krasnogorsk, Moscow Region.
EducationFaculty of Mechanics and Mathematics, MSU, 1996–2001, diploma with honours; postgraduate programme 2001–2004.
Candidate of Physical and Mathematical Sciences (PhD)2005; advisor Professor A. A. Tuzhilin. Thesis: “Geometry of locally minimal and extremal networks in normed spaces”.
PositionAssistant professor, Department of Differential Geometry and Applications, MSU, since 2003.
Research fieldsDifferential geometry; computer geometry; discrete mathematics; variational problems; optimal control theory; low-dimensional topology; knot theory and graph-links.

3. Research

D. P. Ilyutko conducts research in differential geometry, computer geometry, discrete mathematics, variational problems, optimal control theory and low-dimensional topology. His early work was devoted to the geometry of locally minimal and extremal networks in normed and λ-normed spaces, including the structure of branching extremals of the λ-normed length functional and criteria of extremality of trees. Later his main interest shifted to low-dimensional topology: virtual knots, graph-links, parity theory, framed 4-graphs and cross graphs, and their combinatorial invariants.

Main lines of work

  • Geometry of extremal networks in normed and λ-normed spaces; branching extremals of the λ-normed length functional; Maxwell-type formulae for the length of extremal networks.
  • Graph-links and virtual knots: invariants arising from parity, Jones polynomial, cobordisms of free knots, classification problems.
  • Framed 4-graphs, Euler and Gauss circuits, intersection matrices of Euler circuits, and generalized cross graphs.
  • Quasiconformal analysis on Riemannian manifolds: local and boundary behaviour of open discrete mappings (jointly with E. A. Sevostyanov).

4. Teaching and seminars

D. P. Ilyutko has teaching experience at other Moscow universities (MIREA and MFUA). At the Faculty of Mechanics and Mathematics he runs seminars on classical differential geometry, on differential geometry and topology and the practicum in computer geometry, gives a special course in computer geometry, and jointly with V. O. Manturov and I. M. Nikonov leads the special seminar “Knot Theory and Representations”. At various times he has also taught courses in mathematical analysis, algebra and discrete mathematics at other Moscow universities.

He has taken part in numerous conferences, among them the Voronezh Winter Mathematical School (2004), the VIII International Seminar “Discrete Mathematics and Its Applications” (Moscow, 2004), the International Conferences on Analysis and Geometry (Novosibirsk 2004; Novorossiysk 2004, 2006, 2008), the International Conference “Problems of Theoretical Cybernetics” (Penza, 2005), “Contemporary Geometry and Related Topics” (Belgrade, 2005), “Multimedia Technology for Mathematics and Computer Science Education” (Belgrade, 2005), the International Conference on Knot Theory (Heidelberg, 2008) and the Advanced School and Conference on Knot Theory and Its Applications to Physics and Biology (Trieste, 2009).

5. Publications

Full list of publications — 125 records (department page and ISTINA profile)

Books, monographs and textbooks

  1. N. N. Golovanov, D. P. Ilyutko, G. V. Nosovsky, A. T. Fomenko. Computer Geometry. Moscow, Akademiya, 2006.
  2. A. O. Ivanov, D. P. Ilyutko, G. V. Nosovsky, A. A. Tuzhilin, A. T. Fomenko. Computer Geometry: A Practicum. Internet University of Information Technologies, Moscow, 2010, 391 pp.
  3. V. O. Manturov, D. P. Ilyutko. Virtual Knots: The State of the Art. Singapore, World Scientific, 2013, 521 pp.
  4. D. P. Ilyutko, V. O. Manturov, I. M. Nikonov. Combinatorial Topology and Graph Theory in Problems and Exercises. Yaroslavl State University, Yaroslavl, 2013, 150 pp.
  5. D. P. Ilyutko, V. O. Manturov, I. M. Nikonov. Low-Dimensional Topology and Combinatorics in Original Problems. Moscow, 2013, 110 pp.
  6. D. P. Ilyutko, V. O. Manturov, I. M. Nikonov. Parity in Knot Theory and Graph-Links. Plenum Publishers, 2013, 157 pp.
  7. D. P. Ilyutko, V. O. Manturov, I. M. Nikonov. Parity and Patterns in Low-Dimensional Topology. Cambridge Scientific Publishers, 182 pp. ISBN 978-1908106476.
  8. D. P. Ilyutko, I. M. Nikonov. Matrices and Cross Graphs. Polytop, Kaluga, 2021, 160 pp.
  9. D. P. Ilyutko, A. A. Oshemkov. Lectures on the Course of Differential Geometry and Topology. MSU Branch in Baku, Baku, 2022, 120 pp.
  10. N. N. Golovanov, D. P. Ilyutko, G. V. Nosovsky, A. T. Fomenko. Computer Geometry: Foundations of Differential Geometry and Topology. Basic Concepts of Computer Geometry. Geometric Modelling. 2nd ed., URSS, Moscow, 2024, 504 pp.
  11. A. O. Ivanov, D. P. Ilyutko, G. V. Nosovsky, A. A. Tuzhilin, A. T. Fomenko. Computer Geometry: A Practicum. 2nd ed., URSS, Lenand, Moscow, 2024, 384 pp.
  12. D. P. Ilyutko, V. O. Manturov, I. M. Nikonov. Combinatorics and Geometry in Problems and Exercises. MAKS Press, Moscow, 2026, 149 pp.

Papers in books and collections

  1. N-normed planes. In: A. O. Ivanov, A. A. Tuzhilin, Theory of Extremal Networks, Moscow–Izhevsk, 2003, pp. 319–341.
  2. D. P. Ilyutko, V. O. Manturov. Graph-links. In: Introductory Lectures on Knot Theory, ICTP, Trieste, 2009.
  3. D. P. Ilyutko, V. O. Manturov, I. M. Nikonov. Virtual knot invariants arising from parities. Knots in Poland III, Part I, Banach Center Publications, vol. 100 (2014), pp. 99–130.
  4. R. Fenn, D. P. Ilyutko, L. H. Kauffman, V. O. Manturov. Unsolved problems in virtual knot theory and combinatorial knot theory. Knots in Poland III, Part I, Banach Center Publications, vol. 103 (2014), pp. 9–61.

Journal articles

  1. Locally minimal networks in N-normed spaces. Mathematical Notes, 74:5 (2003), pp. 656–668.
  2. Geometry of extremal networks on λ-normed planes. Moscow University Mathematics Bulletin, no. 4 (2005), pp. 52–54.
  3. Branching extremals of the λ-normed length functional. Matematicheskii Sbornik, 197:5 (2006), pp. 75–98.
  4. D. P. Ilyutko, V. O. Manturov. Introduction to graph-link theory. Journal of Knot Theory and Its Ramifications, 18:6 (2009), pp. 791–823.
  5. D. P. Ilyutko, V. O. Manturov. Graph-links. Doklady Mathematics, 80:2 (2009), pp. 739–742.
  6. D. P. Ilyutko, V. O. Manturov. Cobordisms of free knots. Doklady Mathematics, 80:3 (2009), pp. 844–846.
  7. An equivalence between the set of graph-knots and the set of homotopy classes of looped graphs. Journal of Knot Theory and Its Ramifications (2011). DOI 10.1142/S0218216511009649.
  8. Framed 4-graphs: Euler tours, Gauss circuits and rotating circuits. Matematicheskii Sbornik, 202:9 (2011), pp. 53–76.
  9. Intersection matrices of Euler circuits of 4-valent graphs with a cross structure. Matematicheskoe Prosveshchenie, ser. 3, 16 (2012), pp. 105–131.
  10. D. P. Ilyutko, V. O. Manturov, I. M. Nikonov. Parity in knot theory and graph-links. Sovremennaya Matematika. Fundamentalnye Napravleniya, 41 (2011), pp. 3–163; Journal of Mathematical Sciences, 193:6 (2013), pp. 809–965.
  11. A. G. Bannikova, D. P. Ilyutko, I. M. Nikonov. The length of an extremal network in a normed space: the Maxwell formula. Sovremennaya Matematika. Fundamentalnye Napravleniya, 51 (2013), pp. 5–20; Journal of Mathematical Sciences, 214:5 (2016), pp. 593–608.
  12. D. P. Ilyutko, V. O. Manturov, I. M. Nikonov. Graph-links: the state of the art. In: New Ideas in Low-Dimensional Topology, Series on Knots and Everything, vol. 56, World Scientific, 2015, pp. 189–236.
  13. D. P. Ilyutko, V. O. Manturov. A parity map of framed chord diagrams. Journal of Knot Theory and Its Ramifications, 24:13 (2015).
  14. D. P. Ilyutko, E. A. Sevostyanov. On local properties of one class of mappings on Riemannian manifolds. Ukrainian Mathematical Bulletin, 12:2 (2015), pp. 210–221; Journal of Mathematical Sciences, 211:5 (2015), pp. 660–667.
  15. D. P. Ilyutko, V. S. Safina. Graph-links: non-realizability, orientation and the Jones polynomial. Sovremennaya Matematika. Fundamentalnye Napravleniya, 51 (2013), pp. 33–63; Journal of Mathematical Sciences, 214:5 (2016), pp. 632–664.
  16. D. P. Ilyutko, E. A. Sevostyanov. Open discrete mappings with unbounded coefficient of quasiconformality on Riemannian manifolds. Matematicheskii Sbornik, 207:4 (2016), pp. 65–112; Sbornik: Mathematics, 207:4 (2016), pp. 537–580.
  17. D. P. Ilyutko, A. D. Trofimova. 2-coloured diagrams of knots. Lobachevskii Journal of Mathematics, 38:6 (2017), pp. 987–997.
  18. D. P. Ilyutko, I. M. Nikonov. Extremal networks in λ-geometry, where λ = 3, 4, 6. Matematicheskii Sbornik, 208:4 (2017), pp. 17–50; Sbornik: Mathematics, 208:4 (2017), pp. 479–509.
  19. D. P. Ilyutko, E. A. Sevostyanov. Removal of isolated singularities of generalized quasiisometries on Riemannian manifolds. Sovremennaya Matematika. Fundamentalnye Napravleniya, 63:2 (2017), pp. 266–277; Journal of Mathematical Sciences, 250 (2020), pp. 611–621.
  20. D. P. Ilyutko, I. M. Nikonov. The diagram approach in knot theory and applications to graph theory. Moscow University Mathematics Bulletin, 73:3 (2018), pp. 124–130.
  21. D. P. Ilyutko, E. A. Sevostyanov. Boundary behaviour of open discrete mappings on Riemannian manifolds. Matematicheskii Sbornik, 209:5 (2018), pp. 3–53; Sbornik: Mathematics, 209:5 (2018), pp. 605–651.
  22. D. P. Ilyutko, E. A. Sevostyanov. On prime ends on Riemannian manifolds. Ukrainian Mathematical Bulletin, 15:3 (2018), pp. 358–382; Journal of Mathematical Sciences, 241 (2019), pp. 1–17.
  23. D. P. Ilyutko, E. A. Sevostyanov. On the equicontinuity of families of inverse mappings of Riemannian manifolds. Ukrainian Mathematical Bulletin, 16:4 (2019), pp. 557–566; Journal of Mathematical Sciences, 246:5 (2020), pp. 664–670.
  24. D. P. Ilyutko, V. O. Manturov. An invariant of graph-links valued in graphs and an almost classification of graph-links. Journal of Knot Theory and Its Ramifications (2020), 2050063.
  25. D. P. Ilyutko, V. O. Manturov. Picture-valued parity-biquandle bracket. Journal of Knot Theory and Its Ramifications, 29:2 (2020), 2040004.
  26. D. P. Ilyutko, E. A. Sevostyanov. Boundary behaviour of open discrete mappings on Riemannian manifolds. II. Matematicheskii Sbornik, 211:4 (2020), pp. 63–111; Sbornik: Mathematics, 211:4 (2020), pp. 539–582.
  27. S. Yu. Bezgodova, D. P. Ilyutko. Behaviour of the binary rank of a graph under addition of vertices and edges. Moscow University Mathematics Bulletin, no. 6 (2021), pp. 21–26.
  28. D. P. Ilyutko, E. A. Sevostyanov. On the local and boundary behaviour of inverse maps on Riemannian manifolds. Matematicheskii Sbornik, 213:1 (2022), pp. 46–68; Sbornik: Mathematics, 213:1 (2022), pp. 42–62.
  29. V. P. Ilyutko, D. P. Ilyutko. A circle criterion for a generalized cross graph in terms of minimal excluded minors. Matematicheskii Sbornik, 213:12 (2022), pp. 53–67; Sbornik: Mathematics, 213:12 (2022), pp. 1665–1678.
  30. D. P. Ilyutko, I. M. Nikonov. Weight systems of framed chord diagrams corresponding to Lie algebras. Moscow University Mathematics Bulletin, 77:6 (2022), pp. 290–295.
  31. D. P. Ilyutko, V. A. Maslennikova. Linking number for graph-links and some classification of graph-links. Journal of Knot Theory and Its Ramifications, 34:14 (2025), 2540001.
  32. D. P. Ilyutko, E. A. Protasov. The cycle space of the graph of circles for a resolution of a generalized cross graph. Lobachevskii Journal of Mathematics, 46:3 (2025), pp. 1076–1086.

Conference papers (selected)

  1. Locally minimal and extremal networks on N-normed planes. Voronezh Winter Mathematical School, Voronezh, 2004, pp. 82–88.
  2. Extremal networks on Minkowski planes. VIII International Seminar “Discrete Mathematics and Its Applications”, Moscow, 2004, pp. 392–395.
  3. A geometric criterion of extremality of an arbitrary tree on a λ-normed plane. International Conference on Analysis and Geometry, Novosibirsk, 2004, pp. 108–111; Novorossiysk, 2004, pp. 27–29.
  4. λ-realization of a network and convergence of λ-extremal networks as λ → ∞. International Conference “Problems of Theoretical Cybernetics”, Penza, 2005, p. 55.
  5. Branching extremals in λ-geometry. International Conference “Contemporary Geometry and Related Topics”, Belgrade, 2005, p. 32.