Andrey Evgenevich Mironov

Curriculum Vitae

• Born in Novokuznetsk (Kemerovo region, Russia) on October 17, 1974
  
  
• Education:
  Novosibirsk State University, Faculty of Mechanics and Mathematics
  

  1996 1998

  B.Sc. M.Sc.

  
  
• Dissertations:
  

  2002 2011

  Candidate of Science in Physics and Mathematics (PhD), Sobolev Institute of Mathematics. Dissertation title: "Abelian varieties and commuting matrix differential operators". Adviser I.A. Taimanov Doctor of Science in Physics and Mathematics, Sobolev Institute of Mathematics. Dissertation title: "Commuting differential operators and of their applications in the differential geometry"

  
  
• Employment:
  Laboratory of Ill-Posed Processes, Sobolev Institute of Mathematics
  

  1997 - 2003

  Laboratory Assistant, Engineer, Researcher, Senior Researcher

  Laboratory of Dynamical Systems, Sobolev Institute of Mathematics
  

  2003 - 2011 2011 - 2017 2017 - 2021 2021 - up to now

  Senior Researcher Leading Researcher Principal Researcher Acting Director

  Novosibirsk State University, Chair of Geometry and Topology

  1997 - 2004 2004 - 2020 2020 - up to now

  Professor Assistant Associate Professor Professor

  SESC of NSU, Chair of Mathematics

  2018 - up to now

  Head of the chair

  Bogolubov Laboratory of Geometrical Methods in Mathematical Physics, Moscow State University
  

  2010 - 2013

  Leading Researcher

  
  
• Awards and Honors:
  

  2003 - 2008 - 2010 - 2012 - 2013 - 2016 - 2016 - 2022 -

  Prize of the Siberian Mathematical Journal Vekua prize for young scientists of the Siberian Branch of Russian Academy of Sciences A series results obtained by P.G. Grinevich, A.E. Mironov and S.P. Novikov was included into the "List of best results of the Russian Academy of Sciences" Invited speaker of the 6th European Congress of Mathematics in Krakow The results "Supersymmetric 2D Pauli Operators and Burgers hierarchy" by P.G. Grinevich, A.E. Mironov and S.P. Novikov were included into the 5-year report by the President of the Russian Academy of Sciences http://www.ras.ru/news/shownews.aspx?id=30d13c52-9aab-400a-8b04-fa3035236487#content Professor of Russian Academy of Sciences Corresponding member of Russian Academy of Sciences Lyapunov Prize

  
  
• Former PhD students:
  I.P. Rybnikov (with I.A. Taimanov)
  S.V. Agapov
  V.N. Davletshina
  B.T. Saparbayeva
  G.S. Mauleshova
  
  
• Current PhD students:
  M.S. Ermentay
  
  
• Research interests:
  Integrable Systems, Geometry, Mathematical Physics, Dynamical Systems

List of Publications

• Summer School on Geometry and Mathematical Physics, Voskresenskoe, 2012
  "Baker-Akhiezer functions in differential geometry and mathematical physics" (in Russian)
  

1. The moduli space of 2-dimensional algebras.
   Communications in Algebra. 2000. Vol. 28. No. 9. P. 4481-4488 (with A.Z. Ananin).


2. Commutative rings of differential operators connected with two-dimensional abelian varieties.
   Siberian Math. Journal. 2000. Vol. 41. No. 6. P. 1148-1161.


3. On nonlinear equations integrable in theta functions of nonprincipally polarized abelian varieties.
   Siberian Math. Journal. 2001. Vol. 42. No. 1. P. 98-106.


4. Real commuting differential operators connected with two-dimensional abelian varieties.
   Siberian Math. Journal. 2002. Vo;. 43. No. 1. P. 97-113.


5. Commutative rings of differential operators corresponding to multidimensional algebraic varieties.
   Siberian Math. Journal. 2002. Vol. 43, No. 5. P. 888-898.


6. On Hamiltonian-minimal Lagrangian tori in CP².
   Siberian Math. Journal. 2003. Vol. 44. No. 6. P. 1039-1042.


7. On new examples of Hamiltonian-minimal and minimal Lagrangian submanifolds in Cⁿ and CPⁿ.
   Sb. Math. 2004. Vol. 195. No. 1. P.85-96.


8. On Hamiltonian-Minimal and Minimal Lagrangian Submanifolds in Cⁿ and CPⁿ.
   Dokl. Math. 2004. Vol. 69. No. 3. P. 352-354.


9. A ring of commuting differential operators of rank 2 corresponding to a curve of genus 2.
   Sb. Math. 2004. Vol. 195. No. 5. P. 711-722.


10. The Novikov-Veselov hierarchy of equations and integrable deformations of minimal Lagrangian tori in CP².
    Siberian Electronic Mathematical Reports. 2004. Vol. 1. P. 38-46(http://semr.math.nsc.ru in Russian)


11. Spectral subvarieties of a principally polarized Abelian variety.
    Russian Math. Surveys. 2004. Vol. 59. No. 5. P. 969-970.


12. Commuting rank 2 differential operators corresponding to a curve of genus 2.
    Funct. Anal. Appl. 2005. Vol. 39. No. 3. P. 240-243.


13. Orthogonal curvilinear coordinate systems corresponding to singular spectral curves.
    Proceedings of the Steklov Institute of Math. 2006. Vol. 255. P. 169-184 (with I.A. Taimanov).


14. On some algebraic examples of Frobenius manifolds.
    Theoret. and Math. Phys. 2007. Vol. 151. No. 2. P. 604-613 (with I.A. Taimanov).


15. On one family of conformal flat minimal Lagrangian tori in CP³.
    Math. Notes. 2007. Vol. 81. No. 3. P. 329-337.


16. Commuting difference operators with polynomial coefficients.
    Russian Math. Surveys. 2007. Vol. 63. No. 4. P. 819-820.


17. Relationship between symmetries of the Tzitzeica equation and the Novikov-Veselov hierarchy.
    Math. Notes. 2007. Vol. 82. No. 4. P. 569-572.


18. Discrete analogues of the Dixmier operators.
    Sb. Math. 2007. Vol. 19. No. 10. P. 1433-1442.


19. On a Family of Conformally Flat Hamiltonian–Minimal Lagrangian Tori in CP³.
    International Mathematics Research Notices. 2008 Vol. 2008. rnn078 (with Dafeng Zuo).


20. Spectral data for Hamiltonian-minimal Lagrangian tori in CP².
    Proceedings of the Steklov Institute of Math. 2008. Vol. 263. P. 112-126.


21. On commuting differential operators of rank 2.
    Siberian Electronic Mathematical Reports. 2009. Vol. 6. P. 533-536 (http://semr.math.nsc.ru in Russian).


22. On polynomial integrals of a mechanical system on a two-dimensional torus.
    Izvestiya: Mathematics. 2010. Vol. 74. No. 4. P. 805–817.


23. Finite-gap minimal Lagrangian surfaces in CP².
    OCAMI (Osaka City University Advanced Mathematical Institute) Studies Series. 2010. Vol. 3. P. 185-196.


24. Baker-Akhiezer modules on rational varieties.
    SIGMA. 2010. Vol. 6. 030 (with I.A. Melnik).


25. Zero level of a purely magnetic two-dimensional nonrelativistic Pauli operator for spin-1/2 particles.
    Theoretical and Math. Physics. 2010. Vol. 164. No. 3. P. 1110–1127 (with P.G. Grinevich and S.P. Novikov).


26. New Reductions and Nonlinear Systems for 2D Schr\"odinger Operators.
    arXiv: 1001.4300 (with P.G. Grinevich and S.P. Novikov).


27. 2D-Schrodinger Operator, (2+1) evolution systems and new reductions, 2D-Burgers hierarchy and inverse problem data.
    Russian Math. Surveys. 2010. Vol. 164. No. 3. P. 580–582 (with P.G. Grinevich and S.P. Novikov).


28. Baker-Akhiezer 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).


29. Rich quasi-linear system for integrable geodesic flows on 2-torus.
    Discrete and Continuous Dynamical Systems - Series A. 2011. Vol. 29. No. 1. P. 81-90 (with Misha Bialy).


30. Cubic and quartic integrals for geodesic flow on 2-torus via system of hydrodynamic type.
    Nonlinearity. 2011. Vol. 24. P. 3541-3554 (with Misha Bialy).


31. Two-dimensional Pauli operator in magnetic field.
    Low Temperature Physics. 2011. Vol. 37. No. 9-10. P. 829-833 (with P.G. Grinevich and S.P. Novikov).


32. Baker-Akhiezer modules, Krichever sheaves, and commutative rings of partial differential operators.
    Far Eastern Mathematical Journal. 2012. Vol. 12. No. 1. P. 20-34 (with Alexander Zheglov).


33. New semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces.
    Cent. Eur. J. Math. 2012. Vol. 10. No. 5. P. 1596-1604 (with Misha Bialy).


34. Intersections of quadrics, moment-angle manifolds, and Hamiltonian-minimal Lagrangian embeddings.
    Funct. Anal. Appl. 2013. Vol. 47. No. 1. P. 38–49 (with Taras Panov).


35. From polynomial integrals of Hamiltonian flows to a model of non-linear elasticity.
    Journal of Differential Equations. 2013. Vol. 255. No. 10. P. 3434-3446 (with Misha Bialy).


36. Commuting higher rank ordinary differential operators.
    Proceedings of 6th European Congress of Mathematics. 2013. P. 459–473.


37. Hamiltonian-minimal Lagrangian submanifolds in toric varieties.
    Russian Math. Surveys. 2013. Vol. 68. No. 2. P. 392–394 (with Taras Panov).


38. Discretization of Baker-Akhiezer modules and commuting difference operators in several discrete variables.
    Transactions of the Moscow Mathematical Society. 2013. Vol. 74. No. 2. P. 261-279 (with Atsushi Nakayashiki).


39. Self-adjoint commuting ordinary differential operators.
    Inventiones mathematicae. 2014. Vol. 197. No. 2. P. 417-431.


40. Periodic and rapid decay rank two self-adjoint commuting differential operators.
    Amer. Math. Soc. Transl. Ser. 2, 2014. Vol. 234. P. 309-322.


41. Integrable geodesic flows on 2-torus: Formal solutions and variational principle.
    Journal of Geometry and Physics. 2015. Vol. 87. No. 1. P. 39-47 (with Misha Bialy).


42. On the eigenfunctions of the one-dimensional Schrodinger operator with a polynomial potential.
    Doklady Math. 2015. Vol. 91 No. 2. P. 171-172 (with B.T. Saparbayeva).


43. On the nonrelativistic 2D purely magnetic supersymmetric Pauli operator.
    Russian Math. Surveys. 2015. Vol. 70. No. 2. P. 299-329 (with P.G. Grinevich and S.P. Novikov).


44. On commuting differential operators with polynomial coefficients corresponding to spectral curves of genus one.
    Doklady Math. 2015. Vol. 91. No. 3. P. 281-282 (with A.B. Zheglov).


45. Commuting difference operators of rank two.
    Russian Math. Surveys. 2015. Vol. 70. No. 3(423). P. 557 - 559 (with G.S. Mauleshova).


46. One-point commuting difference operators of rank 1.
    Doklady Mathematics. 2016. Vol.93. No. 1. P. 62 - 64 (with G.S. Mauleshova).


47. Commuting ordinary differential operators with polynomial coefficients and automorphisms of the first Weyl algebra.
    International Math. Research Notices. 2016. Vol. 2016. No. 10. P. 2974-2993 (with A.B. Zheglov).


48. Commuting self-adjoint differential operators of rank two.
    Russian Math. Surveys. 2016. Vol. 71. No. 4. P. 751-779.


49. Commuting Krichever-Novikov differential operators with polynomial coefficients.
    Siberian Mathematical Journal. 2016. Vol. 57. No. 5. P. 819-823 (with B.T. Saparbayeva and A.B. Zheglov).


50. On polynomial integrals of the fourth degree of Birkhoff billiard.
    Proc. Steklov Inst. Math. 2016. Vol. 295. P. 27-32 (with M. Bialy).


51. Algebraic non-integrability of magnetic billiards.
    Journal of Physics A: Mathematical and Theoretical". 2016. Vol. 49. No. 45 (with M. Bialy).


52. Algebraic Birkhoff conjecture for billiards on Sphere and Hyperbolic plane.
    Journal of Geometry and Physics. 2017. Vol. 115. P. 150-156 (with M. Bialy.).


53. Spectral curve of the Halphen operator.
    Proceedings of the Edinburgh Mathematical Society. 2017. Vol. 60. No. 2. P. 451-460 (with D. Zuo).


54. Integrable magnetic geodesic flows on 2-torus: new examples via quasi-linear system of PDEs.
    Communications in mathematical physics. 2017. Vol. 351. N. 3. P. 993-1007 (with S.V. Agapov and M. Bialy).


55. Angular billiard and algebraic Birkhoff conjecture.
    Advances in Math. 2017. Vol. 313. P. 102-126 (with M. Bialy).


56. 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. 1669-1675 (with V.N. Davletshina).


57. In search of periodic solutions for a reduction of the Benney chain.
    Journal of Math. Physic. 2017. Vol. 58. No. 11. (with M. Bialy).


58. Energy functional for Lagrangian tori in CP².
    Annals of Global Analysis and Geometry. 2018. vol. 53. No. 4. P. 583-595 (with Hui Ma and D. Zuo).


59. One-point commuting difference operators of rank 1 and their relation with finite-gap Schrodinger operators.
    Doklady Mathematics. 2018. Vol. 97. No. 1. P. 62-64 (with G.S. Mauleshova).


60. 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).


61. 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).


62. On exact solutions of a system of quasi-linear equations describing integrable geodesic flows on a surface.
    Sib. Elektron. Mat. Izv. 2019. Vol. 16. P. 949–954 (with M. G. Abdikalikova).


63. On Rank Two Algebro–Geometric Solutions of an Integrable Chain.
    Trends in Mathematics. 2019. P. 189-195 (with G.S. Mauleshova).


64. Difference Krichever – Novikov operators of rank 2.
    Proc. Steklov Inst. Math. 2019. Vol. 305. P. 195–208 (with G.S. Mauleshova).


65. Periodic One-Point Rank One Commuting Difference Operators.
    Geometric Methods in Physics XXXVIII, Trends in Mathematics, Springer Nature, 2020 (with A. Dobrogowska)


66. 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)


67. Magnetic billiards: Non-integrability for strong magnetic field; Gutkin type examples.
    Journal of Geometry and Physics. 2020. Vol. 154. 19 pp. (103716) (with M. Bialy and L. Shalom)


68. Wire billiards, the first steps.
    Advances in Mathematics. 2020. Vol. 368. 30 pp. (107154) (with M. Bialy and S. Tabachnikov)


69. 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)


70. Outer Billiards with the Dynamics of a Standard Shift on a Finite Number of Invariant Curves.
    Experimental Mathematics. 2021. Vol. 30. No. 4. P. 469-474 (with M. Bialy and L. Shalom)


71. The Birkhoff-Poritsky conjecture for centrally-symmetric billiard tables.
    Annals of Mathematics. 2022. Vol. 196. No. 1. P. 389-413 (with M. Bialy)


72. Orthogonal curvilinear coordinate systems and torsion-free sheaves over reducible spectral curves.
    Mathematical Notes. 2023. Vol. 114. No. 4. P. 573–582 (with A. Senninger and I.A. Taimanov)


73. One-dimensional finite-gap Schrodinger operators as a limit of commuting difference operators.
    Doklady Mathematics. 2023. Vol. 108. No. 1. P. 312–315 (with G.S. Mauleshova)


74. On Differential Equations of Integrable Billiard Tables.
    Acta Mathematica Sinica. 2024. Vol. 40. No. 1. P. 417-424 (with V. Dragovic)


75. Difference analogue of the Lame operator.
    Proc. Steklov Inst. Math. 2024. (with V. Mauleshova)