List of Publications
 The moduli space of 2dimensional algebras.
Communications in Algebra. 2000. Vol. 28. No. 9. P. 44814488 (with A.Z. Ananin).
 Commutative rings of differential operators connected with twodimensional abelian varieties.
Siberian Math. Journal. 2000. Vol. 41. No. 6. P. 11481161.
 On nonlinear equations integrable in theta functions of nonprincipally polarized abelian varieties.
Siberian Math. Journal. 2001. Vol. 42. No. 1. P. 98106.
 Real commuting differential operators connected with twodimensional abelian varieties.
Siberian Math. Journal. 2002. Vo;. 43. No. 1. P. 97113.
 Commutative rings of differential operators corresponding to multidimensional algebraic varieties.
Siberian Math. Journal. 2002. Vol. 43, No. 5. P. 888898.
 On Hamiltonianminimal Lagrangian tori in CP^{2}.
Siberian Math. Journal. 2003. Vol. 44. No. 6. P. 10391042.
 On new examples of Hamiltonianminimal and minimal Lagrangian submanifolds in C^{n} and CP^{n}.
Sb. Math. 2004. Vol. 195. No. 1. P.8596.
 On HamiltonianMinimal and Minimal Lagrangian Submanifolds in C^{n} and CP^{n}.
Dokl. Math. 2004. Vol. 69. No. 3. P. 352354.
 A ring of commuting differential operators of rank 2 corresponding to a curve of genus 2.
Sb. Math. 2004. Vol. 195. No. 5. P. 711722.
 The NovikovVeselov hierarchy of equations and integrable deformations of minimal Lagrangian tori in CP^{2}.
Siberian Electronic Mathematical Reports. 2004. Vol. 1. P. 3846(http://semr.math.nsc.ru in Russian)
 Spectral subvarieties of a principally polarized Abelian variety.
Russian Math. Surveys. 2004. Vol. 59. No. 5. P. 969970.
 Commuting rank 2 differential operators corresponding to a curve of genus 2.
Funct. Anal. Appl. 2005. Vol. 39. No. 3. P. 240243.
 Orthogonal curvilinear coordinate systems corresponding to singular spectral curves.
Proceedings of the Steklov Institute of Math. 2006. Vol. 255. P. 169184 (with I.A. Taimanov).
 On some algebraic examples of Frobenius manifolds.
Theoret. and Math. Phys. 2007. Vol. 151. No. 2. P. 604613 (with I.A. Taimanov).
 On one family of conformal flat minimal Lagrangian tori in CP^{3}.
Math. Notes. 2007. Vol. 81. No. 3. P. 329337.
 Commuting difference operators with polynomial coefficients.
Russian Math. Surveys. 2007. Vol. 63. No. 4. P. 819820.
 Relationship between symmetries of the Tzitzeica equation and the NovikovVeselov hierarchy.
Math. Notes. 2007. Vol. 82. No. 4. P. 569572.
 Discrete analogues of the Dixmier operators.
Sb. Math. 2007. Vol. 19. No. 10. P. 14331442.
 On a Family of Conformally Flat Hamiltonian–Minimal Lagrangian Tori in CP^{3}.
International Mathematics Research Notices. 2008 Vol. 2008. rnn078 (with Dafeng Zuo).
 Spectral data for Hamiltonianminimal Lagrangian tori in CP^{2}.
Proceedings of the Steklov Institute of Math. 2008. Vol. 263. P. 112126.
 On commuting differential operators of rank 2.
Siberian Electronic Mathematical Reports. 2009. Vol. 6. P. 533536 (http://semr.math.nsc.ru in Russian).
 On polynomial integrals of a mechanical system on a twodimensional torus.
Izvestiya: Mathematics. 2010. Vol. 74. No. 4. P. 805–817.
 Finitegap minimal Lagrangian surfaces in CP^{2}.
OCAMI (Osaka City University Advanced Mathematical Institute) Studies Series. 2010. Vol. 3. P. 185196.
 BakerAkhiezer modules on rational varieties.
SIGMA. 2010. Vol. 6. 030 (with I.A. Melnik).
 Zero level of a purely magnetic twodimensional nonrelativistic Pauli operator for spin1/2 particles.
Theoretical and Math. Physics. 2010. Vol. 164. No. 3. P. 1110–1127 (with P.G. Grinevich and S.P. Novikov).
 New Reductions and Nonlinear Systems for 2D Schr\"odinger Operators.
arXiv: 1001.4300 (with P.G. Grinevich and S.P. Novikov).
 2DSchrodinger Operator, (2+1) evolution systems and new reductions, 2DBurgers hierarchy and inverse problem data.
Russian Math. Surveys. 2010. Vol. 164. No. 3. P. 580–582 (with P.G. Grinevich and S.P. Novikov).
 BakerAkhiezer Modules on the Intersections of Shifted Theta Divisors .
Publications of the Research Institute for Mathematical Sciences. 2011. Vol. 47. No. 2. P. 353–567 (with Koji Cho and Atsushi Nakayashiki).
 Rich quasilinear system for integrable geodesic flows on 2torus.
Discrete and Continuous Dynamical Systems  Series A. 2011. Vol. 29. No. 1. P. 8190 (with Misha Bialy).
 Cubic and quartic integrals for geodesic flow on 2torus via system of hydrodynamic type.
Nonlinearity. 2011. Vol. 24. P. 35413554 (with Misha Bialy).
 Twodimensional Pauli operator in magnetic field.
Low Temperature Physics. 2011. Vol. 37. No. 910. P. 829833 (with P.G. Grinevich and S.P. Novikov).
 BakerAkhiezer modules, Krichever sheaves, and commutative rings of partial differential operators.
Far Eastern Mathematical Journal. 2012. Vol. 12. No. 1. P. 2034 (with Alexander Zheglov).
 New semiHamiltonian hierarchy related to integrable magnetic flows on surfaces.
Cent. Eur. J. Math. 2012. Vol. 10. No. 5. P. 15961604 (with Misha Bialy).
 Intersections of quadrics, momentangle manifolds, and Hamiltonianminimal Lagrangian embeddings.
Funct. Anal. Appl. 2013.
Vol. 47. No. 1. P. 38–49 (with Taras Panov).
 From polynomial integrals of Hamiltonian flows to a model of nonlinear elasticity.
Journal of Differential Equations. 2013. Vol. 255. No. 10. P. 34343446 (with Misha Bialy).
 Commuting higher rank ordinary differential operators.
Proceedings of 6th European Congress of Mathematics. 2013. P. 459–473.
 Hamiltonianminimal Lagrangian submanifolds in toric varieties.
Russian Math. Surveys. 2013. Vol. 68. No. 2. P. 392–394 (with Taras Panov).
 Discretization of BakerAkhiezer modules and commuting difference operators in several discrete variables.
Transactions of the Moscow Mathematical Society. 2013. Vol. 74. No. 2. P. 261279 (with Atsushi Nakayashiki).
 Selfadjoint commuting ordinary differential operators.
Inventiones mathematicae. 2014. Vol. 197. No. 2. P. 417431.
 Periodic and rapid decay rank two selfadjoint commuting differential operators.
Amer. Math. Soc. Transl. Ser. 2, 2014. Vol. 234. P. 309322.
 Integrable geodesic flows on 2torus: Formal solutions and variational principle.
Journal of Geometry and Physics. 2015. Vol. 87. No. 1. P. 3947 (with Misha Bialy).
 On the eigenfunctions of the onedimensional Schrodinger operator with a polynomial potential.
Doklady Math. 2015. Vol. 91 No. 2. P. 171172 (with B.T. Saparbayeva).
 On the nonrelativistic 2D purely magnetic supersymmetric Pauli operator.
Russian Math. Surveys. 2015. Vol. 70. No. 2. P. 299329 (with P.G. Grinevich and S.P. Novikov).
 On commuting differential operators with polynomial coefficients corresponding to spectral curves of genus one.
Doklady Math. 2015. Vol. 91. No. 3. P. 281282 (with A.B. Zheglov).
 Commuting difference operators of rank two.
Russian Math. Surveys. 2015. Vol. 70. No. 3(423). P. 557  559 (with G.S. Mauleshova).
 Onepoint commuting difference operators of rank 1.
Doklady Mathematics. 2016. Vol.93. No. 1. P. 62  64 (with G.S. Mauleshova).
 Commuting ordinary differential operators with polynomial coefficients and automorphisms of the first Weyl algebra.
International Math. Research Notices. 2016. Vol. 2016. No. 10. P. 29742993 (with A.B. Zheglov).
 Commuting selfadjoint differential operators of rank two.
Russian Math. Surveys. 2016. Vol. 71. No. 4. P. 751779.
 Commuting KricheverNovikov differential operators with polynomial coefficients.
Siberian Mathematical Journal. 2016. Vol. 57. No. 5. P. 819823 (with B.T. Saparbayeva and A.B. Zheglov).
 On polynomial integrals of the fourth degree of Birkhoff billiard.
Proc. Steklov Inst. Math. 2016. Vol. 295. P. 2732 (with M. Bialy).
 Algebraic nonintegrability of magnetic billiards.
Journal of Physics A: Mathematical and Theoretical". 2016. Vol. 49. No. 45 (with M. Bialy).
 Algebraic Birkhoff conjecture for billiards on Sphere and Hyperbolic plane.
Journal of Geometry and Physics. 2017. Vol. 115. P. 150156 (with M. Bialy.).
 Spectral curve of the Halphen operator.
Proceedings of the Edinburgh Mathematical Society. 2017. Vol. 60. No. 2. P. 451460 (with D. Zuo).
 Integrable magnetic geodesic flows on 2torus: new examples via quasilinear system of PDEs.
Communications in mathematical physics. 2017. Vol. 351. N. 3. P. 9931007 (with S.V. Agapov and M. Bialy).
 Angular billiard and algebraic Birkhoff conjecture.
Advances in Math. 2017. Vol. 313. P. 102126 (with M. Bialy).
 On commuting ordinary differential operators with polynomial coefficients corresponding to spectral curves of genus two.
Bull. Korean Math. Soc. 2017. Vol. 54. No. 5. P. 16691675 (with V.N. Davletshina).
 In search of periodic solutions for a reduction of the Benney chain.
Journal of Math. Physic. 2017. Vol. 58. No. 11. (with M. Bialy).
 Energy functional for Lagrangian tori in CP^{2}.
Annals of Global Analysis and Geometry. 2018. vol. 53. No. 4. P. 583595 (with Hui Ma and D. Zuo).
 Onepoint commuting difference operators of rank 1 and their relation with finitegap
Schrodinger operators.
Doklady Mathematics. 2018. Vol. 97. No. 1. P. 6264 (with G.S. Mauleshova).
 A survey on polynomial in momenta integrals for billiard ploblems.
Philosophical Transactions of the royal society A. Math., phys. and engineering sciences. 2018. Vol. 376. No. 2131. A.N. 20170418 (with M. Bialy).
 Polynomial nonintegrability of magnetic billards on the sphere and hyperbolic plane.
Russian Math. Surveys. 2019. Vol. 74. No. 2. P. 187–209 (with M. Bialy).
 On exact solutions of a system of quasilinear equations describing integrable geodesic flows on a surface.
Sib. Elektron. Mat. Izv. 2019. Vol. 16. P. 949–954 (with M. G. Abdikalikova).
 On Rank Two Algebro–Geometric Solutions of an Integrable Chain.
Trends in Mathematics. 2019. P. 189195 (with G.S. Mauleshova).
 Difference Krichever – Novikov operators of rank 2.
Proc. Steklov Inst. Math. 2019. Vol. 305. P. 195–208 (with G.S. Mauleshova).
 Outer Billiards with the Dynamics of a Standard Shift on a Finite Number of Invariant Curves.
Experimental Mathematics. 2019 (Published online) (with M. Bialy and L. Shalom)
 Periodic OnePoint Rank One Commuting Difference Operators.
Geometric Methods in Physics XXXVIII, Trends in Mathematics, Springer Nature, 2020 (with A. Dobrogowska)
 Positive one–point commuting difference operators.
Integrable Systems and Algebraic Geometry, Part of London Mathematical Society Lecture Note Series, 1, Cambridge University Press. 2020. P. 395–412 (with G.S. Mauleshova)
 Magnetic billiards: Nonintegrability for strong magnetic field; Gutkin type examples.
Journal of Geometry and Physics. 2020. Vol. 154. 19 pp. (103716) (with M. Bialy and L. Shalom)
 Wire billiards, the first steps.
Advances in Mathematics. 2020. Vol. 368. 30 pp. (107154) (with M. Bialy and S. Tabachnikov)
 Discretization of Commuting Ordinary Differential Operators of Rank 2 in the Case of Elliptic Spectral Curves.
Proc. Steklov Inst. Math. 2020. Vol. 310. (with G.S. Mauleshova)
