1. Pentagram maps over rings, Grassmannians, and skewers. with L. Hand, arXiv:2405.06122

  2. Planar networks and simple Lie groups beyond type A. arXiv:2308.13975


  1. Coadjoint orbits of area-preserving diffeomorphisms of non-orientable surfaces. with B. Khesin and I. Kirillov, Journal of Symplectic Geometry, to appear

  2. Geometry of generalized fluid flows. with B. Khesin, Calculus of Variations and Partial Differential Equations, vol. 63, no. 3 (2024)

  3. Change of polytope volumes under Möbius transformations and the circumcenter of mass. Discrete & Computational Geometry, (2023)

  4. Long-diagonal pentagram maps. with B. Khesin, Bulletin of the London Mathematical Society, vol .55, no. 3 (2023), 1314-1329

  5. Polygon recutting as a cluster integrable system. Selecta Mathematica, vol. 29, no. 21 (2023)

  6. Jordan-Kronecker invariants of Lie algebra representations and degrees of invariant polynomials. with A. Bolsinov and I. Kozlov, Transformation Groups, vol. 28 (2023), 541-560

  7. What is a lattice W-algebra? with G. Marí Beffa, International Mathematics Research Notices, vol. 2023, no. 19 (2023), 17021-17059

  8. Dimers, networks, and cluster integrable systems. Geometric and Functional Analysis, vol. 32 (2022), 861-880

  9. The pentagram map, Poncelet polygons, and commuting difference operators. Compositio Mathematica, vol. 158, no. 5 (2022), 1084-1124

  10. Pentagram maps and refactorization in Poisson-Lie groups. Advances in Mathematics, vol. 404 (2022), 108476

  11. Intersecting the sides of a polygon. Proceedings of the American Mathematical Society, vol. 150 (2022), 639-649

  12. The limit point of the pentagram map and infinitesimal monodromy. with Q. Aboud, International Mathematics Research Notices, vol. 2022, no. 7 (2022), 5383-5397

  13. Smooth invariants of focus-focus singularities and obstructions to product decomposition. with A. Bolsinov, Journal of Symplectic Geometry, vol. 17, no. 6 (2019), 1613-1648

  14. Vortex sheets and diffeomorphism groupoids. with B. Khesin, Advances in Mathematics, vol. 338 (2018), 447-501

  15. Characterization of steady solutions to the 2D Euler equation. with B. Khesin, International Mathematics Research Notices, vol. 2017, no.24 (2017), 7459-7503

  16. Singularities of integrable systems and algebraic curves. International Mathematics Research Notices, vol. 2017, no. 18 (2017), 5475-5524

  17. Classification of Casimirs in 2D hydrodynamics. with B. Khesin, Moscow Math Journal, vol.17, no.4 (2017), 699-716

  18. Finite-dimensional integrable systems: a collection of research problems. with A. Bolsinov and D. Tsonev, Journal of Geometry and Physics, vol. 115 (2017), 2-15

  19. Euler equations on the general linear group, cubic curves, and inscribed hexagons. with K. Aleshkin, L'Enseignement Mathématique, vol. 62 (2016), 143-170

  20. Coadjoint orbits of symplectic diffeomorphisms of surfaces and ideal hydrodynamics. with B. Khesin and M. Mousavi, Annales de l'Institut Fourier, vol.66, no.6 (2016), 2385-2433

  21. Pentagrams, inscribed polygons, and Prym varieties. Electronic Research Announcements in Mathematical Sciences, vol. 23 (2016), 25-40

  22. Flat bi-Hamiltonian structures and invariant densities. Letters in Mathematical Physics, vol. 106 (2016), 1415-1427

  23. Leapfrog map and Toda lattice. appendix to "Integrable cluster dynamics of directed networks and pentagram maps" by M. Gekhtman, M. Shapiro, S. Tabachnikov, and A. Vainshtein, Advances in Mathematics, vol. 300 (2016), 390-450

  24. Algebraic geometry and stability for integrable systems. Physica D, vol. 291 (2015), 74-82

  25. Singularities of bi-Hamiltonian systems. with A. Bolsinov, Communications in Mathematical Physics, vol. 331 (2014), 507-543

  26. Stability of relative equilibria of multidimensional rigid body. Nonlinearity, vol. 27 (2014), 1419-1444

  27. The derived algebra of a stabilizer, families of coadjoint orbits, and sheets. Journal of Lie Theory, vol. 24 (2014), 705-714

  28. Curvature of Poisson pencils in dimension three. Differential Geometry and its Applications, vol. 31 (2013), 557-567

  29. Stability of stationary rotations of multidimensional rigid body, Moscow University Mathematics Bulletin, vol. 68 (2013), 80-82

  30. Stability in bihamiltonian systems and multidimensional rigid body. Journal of Geometry and Physics, vol. 62 (2012), 2414-2423

  31. A note on relative equilibria of a free multidimensional rigid body. Journal of Physics A: Mathematical and Theoretical, vol. 45 (2012), 325203

  32. Algebra and topology of integrable systems: problems for investigation. with A. Bolsinov, A. Konyaev, and A. Oshemkov, Tr. Sem. Vektor Tenzor Anal (in Russian), vol. 28 (2012), 119-191

  33. Classification of almost toric singularities of Lagrangian foliations. Sbornik: Mathematics, vol. 202 (2011), 1021-1042

  34. Smooth invariants of focus-focus singularities. Moscow University Mathematics Bulletin, vol. 66 (2011), 178-180

 Unpublished notes

  1. Matrix polynomials, generalized Jacobians, and graphical zonotopes, arXiv:1506.05179

  2. Singularities of integrable systems and nodal curves, arXiv:1408.4844

  3. Generalized argument shift method and complete commutative subalgebras in polynomial Poisson algebras, arXiv:1406.3777