Preprints
Planar networks and simple Lie groups beyond type A. arXiv:2308.13975
Coadjoint orbits of area-preserving diffeomorphisms of non-orientable surfaces. with B. Khesin and I. Kirillov, to appear in Journal of Symplectic Geometry (2024)
Papers
Integrable systems and cluster algebras. with M. Gekhtman, Encyclopedia of Mathematical Physics, 2nd edition (2024)
Geometry of generalized fluid flows. with B. Khesin, Calculus of Variations and Partial Differential Equations, vol. 63, no. 3 (2024)
Change of polytope volumes under Möbius transformations and the circumcenter of mass. Discrete & Computational Geometry, https://doi.org/10.1007/s00454-022-00481-x (2023)
Long-diagonal pentagram maps. with B. Khesin, Bulletin of the London Mathematical Society, vol .55, no. 3 (2023), 1314-1329
Polygon recutting as a cluster integrable system. Selecta Mathematica, vol. 29, no. 21 (2023)
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
What is a lattice W-algebra? with G. Marí Beffa, International Mathematics Research Notices, vol. 2023, no. 19 (2023), 17021-17059
Dimers, networks, and cluster integrable systems. Geometric and Functional Analysis, vol. 32 (2022), 861-880
The pentagram map, Poncelet polygons, and commuting difference operators. Compositio Mathematica, vol. 158, no. 5 (2022), 1084-1124
Pentagram maps and refactorization in Poisson-Lie groups. Advances in Mathematics, vol. 404 (2022),
108476
Intersecting the sides of a polygon. Proceedings of the American Mathematical Society, vol. 150 (2022), 639-649 The limit point of the pentagram map and infinitesimal monodromy. with Q. Aboud, International Mathematics Research Notices, vol. 2022, no. 7 (2022), 5383-5397
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
Vortex sheets and diffeomorphism groupoids. with B. Khesin, Advances in Mathematics, vol. 338 (2018), 447-501
Characterization of steady solutions to the 2D Euler equation. with B. Khesin, International Mathematics Research Notices, vol. 2017, no.24 (2017), 7459-7503
Singularities of integrable systems and algebraic curves. International Mathematics Research Notices, vol. 2017, no. 18 (2017), 5475-5524
Classification of Casimirs in 2D hydrodynamics. with B. Khesin, Moscow Math Journal, vol.17, no.4 (2017), 699-716
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
Euler equations on the general linear group, cubic curves, and inscribed hexagons. with K. Aleshkin, L'Enseignement Mathématique, vol. 62 (2016), 143-170
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
Pentagrams, inscribed polygons, and Prym varieties. Electronic Research Announcements in Mathematical Sciences, vol. 23 (2016), 25-40
Flat bi-Hamiltonian structures and invariant densities. Letters in Mathematical Physics, vol. 106 (2016), 1415-1427
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
Algebraic geometry and stability for integrable systems. Physica D, vol. 291 (2015), 74-82
Singularities of bi-Hamiltonian systems. with A. Bolsinov,
Communications in Mathematical Physics, vol. 331 (2014), 507-543
Stability of relative equilibria of multidimensional rigid body. Nonlinearity, vol. 27 (2014), 1419-1444
The derived algebra of a stabilizer, families of coadjoint orbits, and sheets. Journal of Lie Theory, vol. 24 (2014), 705-714
Curvature of Poisson pencils in dimension three. Differential Geometry and its Applications, vol. 31 (2013), 557-567
Stability of stationary rotations of multidimensional rigid body, Moscow University Mathematics Bulletin, vol. 68 (2013), 80-82
Stability in bihamiltonian systems and
multidimensional rigid body. Journal of Geometry and Physics, vol. 62 (2012), 2414-2423
A note on relative equilibria of a free
multidimensional rigid body. Journal of Physics A: Mathematical and Theoretical, vol. 45 (2012), 325203
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
Classification of almost toric singularities of Lagrangian foliations. Sbornik: Mathematics, vol. 202 (2011), 1021-1042
Smooth invariants of focus-focus singularities.
Moscow University Mathematics Bulletin, vol. 66 (2011), 178-180
Unpublished notes