Books and papers by Boris Khesin:

Books

3. Geometry of infinite-dimensional groups. with Robert Wendt, Ergebnisse der Mathematik und Grenzgebiete 3.Folge, 51, Springer-Verlag, 2009, xviii+304pp.; Russian edition: MCCME 2014, 368pp. ( Introduction and table of contents , extended Lecture notes )

2. Lectures on topological fluid mechanics. (with M.Berger, L.Kauffman, K.Moffatt, R.Ricca, and De W.Sumners) Lecture Notes in Math., 1973, Springer-Verlag, 2009, 221pp.

1. Topological methods in hydrodynamics. with Vladimir I. Arnold, Applied Math. Series 125, Springer-Verlag, 1998, xv+374pp.; Second printing 1999, xv+376pp.; Russian edition: MCCME 2007, 392pp. ( Introduction and table of contents, Chapters 1, 2, 3, 4, 5, 6, Bibliography, Index); Russian extended second edition: MCCME 2020, 456pp.; English extended edition: Springer Nature Switzerland AG, 2021, 455pp., Bulletin AMS Book Review vol. 60:2 (2023) by G.Misiolek and EMS Magazin Book Review vol. 128 (2023) by D.Peralta-Salas)

Books translated

1. Fundamentals of geophysical hydrodynamics. by Felix V. Dolzhansky, Encyclopaedia of Math. Sci.: Mathematical Physics 103, Springer-Verlag, 2013, xiv+272pp.


Papers

97. The Euler non-mixing made easy. preprint arXiv:2402.08836, (2024), 4pp.

96. Singular vortex pairs follow magnetic geodesics. with Theodore Drivas and Daniil Glukhovskiy, preprint arXiv:2401.08512, (2024), 14pp.

95. Information geometry of diffeomorphism groups. with Gerard Misiolek, preprint, submitted to Handbook of Information Geometry, Geometric Foundation (2022), 48pp.

94. Simple unbalanced optimal transport. with Klas Modin and Luke Volk, Int. Math. Research Notices (IMRN), (2024), 17pp; https://doi.org/10.1093/imrn/rnae020, arXiv:2307.05703

93. Coadjoint orbits of area-preserving diffeomorphisms of non-orientable surfaces. with Anton Izosimov and Ilia Kirillov, to appear in J. of Symplectic Geometry, arXiv:2304.09354, (2024), 23pp.

92. Geometry of generalized fluid flows. with Anton Izosimov, Calc. Var. Partial Differential Equations, vol.63:3 (2023), 30pp.; https://doi.org/10.1007/s00526-023-02612-5; arXiv:2206.01434

91. The Toda flow as a porous medium equation. with Klas Modin, Comm. Math. Physics (CMP), vol.401 (2023), 1879-1898; arXiv:2207.10214

90. Geometric hydrodynamics in open problems. with Gerard Misiolek and Alexander Shnirelman, Arch. Rational Mech. Anal. (ARMA), (2023), 247:15, 43pp., DOI: 10.1007/s00205-023-01848-x; arXiv:2205.01143

89. Long-diagonal pentagram maps. with Anton Izosimov, Bulletin of the London Math. Soc., vol.55, no.3 (2023), 1314-1329; arXiv:2203.07578

88. Quartic Oscillators. SCGP News, vol.XVII-XVIII (2022), 28-29.

87. The helicity uniqueness conjecture in 3D hydrodynamics. with Daniel Peralta-Salas and Cheng Yang, Trans. of the Amer. Math. Soc., vol.375, no.2 (2022), 909-924; arXiv:2003.06008

86. The golden ratio and hydrodynamics. with Hanchun Wang, The Mathematical Intelligencer (TMIN), vol.44, no.1 (2022), 22-27; arXiv:2104.02225

85. Geometric hydrodynamics and infinite-dimensional Newton's equations. with Gerard Misiolek and Klas Modin, Bulletin of the Amer. Math. Soc., vol.58, no.3 (2021), 377-442; arXiv:2001.01143

84. Higher-dimensional Euler fluids and Hasimoto transform: counterexamples and generalizations. with Cheng Yang, Nonlinearity, vol.34, no.3 (2021), 1525-1542, arXiv:1902.08834

83. Lectures on pentagram maps and KdV hierarchies. Proceedings of the Gokova Geometry-Topology Conferences, 2018/2019 (Ed: S.Akbulut et al), International Press (2021), 164-175.

82. Polar bear or penguin? Musings on Earth cartography and Chebyshev nets. with Sergei Tabachnikov, The Mathematical Intelligencer (TMIN), vol.43, no.1 (2021), 20-24.

81. ¿Entiendes realmente la cartografía de la Tierra? (Do you really understand the Earth cartography?) EL PAÍS, Aug.12, 2020, 4pp.

80. On the 80th Birthday of Dmitry Borisovich Fuchs. (with A.Fialowski, Ek.Fuchs, El.Fuchs, F.Malikov et al) SIGMA, vol.16 (2020), 023, 17pp.; arXiv:2004:03270

79. Global, local and dense non-mixing of the 3D Euler equation. with Sergei Kuksin and Daniel Peralta-Salas, Arch. Rational Mech. Anal. (ARMA), vol.238 (2020), 1087-1112; arXiv:1911.04363

78. A basis of Casimirs in 3D magnetohydrodynamics. with Daniel Peralta-Salas and Cheng Yang, Int. Math. Research Notices (IMRN), vol.2021, no.18 (2021), 13645-13660, arXiv:1901.04404

77. Averaging, symplectic reduction, and central extensions. with Cheng Yang, Nonlinearity, vol.33 (2020), 1342-1365; arXiv:1806.01755

76. ¿Es posible ser 1/3 español? (Is it possible to be 1/3 Spanish?) EL PAÍS, Nov.22, 2019, 3pp.

75. Fun problems in geometry and beyond. with Sergei Tabachnikov, SIGMA, vol.15 (2019), 097, 21pp., arXiv:1912.05740

74. Geometry of the Madelung transform. with Gerard Misiolek and Klas Modin, Arch. Rational Mech. Anal. (ARMA), vol.234 (2019), 549-573; arXiv:1807.07172

73. Geometric hydrodynamics via Madelung transform. with Gerard Misiolek and Klas Modin, Proc. Nat. Acad. Sci., vol.115, no.24 (2018), 6165-6170; arXiv:1711.00321

72. Vladimir Igorevich Arnold. with Sergei Tabachnikov, Biographical Memoirs Fell. R. Soc., vol.64 (2018), 7-26; DOI: 10.1098/rsbm.2017.0016

71. Vortex sheets and diffeomorphism groupoids. with Anton Izosimov, Advances in Math., vol.338 (2018), 447-501; arXiv:1705.01603

70. Classification of Casimirs in 2D hydrodynamics. with Anton Izosimov, Moscow Math Journal, vol.17, no.4 (2017), 699-716; arXiv:1702.01843

69. Characterization of steady solutions to the 2D Euler equation. with Anton Izosimov, Int. Math. Research Notices (IMRN), vol.2017, no.24 (2017), 7459-7503; arXiv:1511.05623

68. Coadjoint orbits of symplectic diffeomorphisms of surfaces and ideal hydrodynamics. with Anton Izosimov and Mehdi Mousavi, Annales de l'Institut Fourier, vol.66, no.6 (2016), 2385-2433; arXiv:1504.05629

67. The geometry of dented pentagram maps. with Fedor Soloviev, J. Europ. Math. Soc., vol. 18 (2016), 147-179; arXiv:1308.5363;

66. Non-integrability vs. integrability in pentagram maps. with Fedor Soloviev, J. of Geometry and Physics, vol. 87 (2015), 275-285; (arXiv:1404.6221)

65. Vortex filaments and the Hasimoto transform. in Proceedings of Shape Analysis Workshop in Bad Gastein (2014), preprint hal-01076953, 19-22;

64. Comments on "A Mathematical Trivium" by V.Arnold. with Serge Tabachnikov, in ARNOLD: Swimming Against the Tide., Amer. Math. Soc. (2014), 57-66;

63. KAM theory and the 3D Euler equation. with Sergei Kuksin and Daniel Peralta-Salas, Advances in Math., vol. 267 (2014), 498-522; (arXiv:1401.5516)

62. The vortex filament equation in any dimension. Procedia IUTAM, vol. 7 (2013), 135-140;

61. Integrability of higher pentagram maps. with Fedor Soloviev, Mathem. Annalen, vol. 357 (2013), 1005-1047; (arXiv:1204.0756)

60. Curvatures of Sobolev metrics on diffeomorphism groups. with Jonatan Lenells, Gerard Misiolek, and Stephen C. Preston, Pure and Appl. Math. Quaterly, vol.9, no.2 (2013), 291-332; (arXiv:1109.1816)

59. Geometry of diffeomorphism groups, complete integrability and geometric statistics. with Jonatan Lenells, Gerard Misiolek, and Stephen C. Preston, Geom. and Funct. Anal., vol.23, no.1 (2013), 334-366; (arXiv:1105.0643)

58. The Euler and Navier-Stokes equations on the hyperbolic plane. with Gerard Misiolek, Proc. Nat. Acad. Sci., vol. 109, no.45 (2012), 18324-18326; (arXiv:1205.5322)

57. The pentagram map in higher dimensions and KdV flows. with Fedor Soloviev, Electron. Res. Announc. Math. Sci. (ERA-MS), vol.19 (2012), 86-96; (arXiv:1205.3744)

56. On V.I.Arnold and hydrodynamics. Notices of the AMS, vol. 59 (2012), 492-495.

55. Symplectic structures and dynamics on vortex membranes. Moscow Math. Journal, vol.12, no.2 (2012), 413-434; (arXiv:1201.5914)

54. Dynamics of symplectic fluids and point vortices. Geom. and Funct. Anal., vol.22, no.5 (2012), 1444-1459; (arXiv:1106.1609)

53. Discrete spherical means of directional derivatives and Veronese maps. with Alexander Belyaev and Serge Tabachnikov, J. of Geometry and Physics, vol.62 (2012), 124-136; (arXiv:1106.3691)

52. Contact complete integrability. with Serge Tabachnikov, Regular and Chaotic Dynamics, vol.15, no.4-5 (2010), 504-520; (arXiv:0910.0375)

51. A nonholonomic Moser theorem and optimal mass transport. with Paul Lee, J. of Sympl. Geometry, vol.7, no.4 (2009), 381-414; (arXiv:0802.1551)

50. Pseudo-Riemannian geodesics and billiards. with Sergei Tabachnikov, Advances in Math., vol. 221 (2009), 1364-1396; (math.DG/0608620)

49. Generalized Hunter-Saxton equation and the geometry of the group of circle diffeomorphisms. with Jonatan Lenells and Gerard Misiolek, Mathem. Annalen, vol.342 (2008), 617-656; (arXiv:0803.3078)

48. Groups and topology in the Euler hydrodynamics and KdV. in Hamiltonian dynamical systems and applications, Ed. W.Craig, NATO Science series B, XVI Springer-Verlag (2008), 93-102; The group and Hamiltonian descriptions of hydrodynamical systems. CIME lectures, 16pp.

47. Poisson geometry and first integrals of geostrophic equations. with Paul Lee, Physica D, vol.237 (2008), 2072-2077; (arXiv:0802.4439)

46. Geodesics on an ellipsoid in Minkowski space. with Daniel Genin and Sergei Tabachnikov, L'Enseignement Mathématique, vol. 53 (2007), 307-331; (arXiv:0705.0188)

45. Shock waves for the Burgers equation and curvatures of diffeomorphism groups. with Gerard Misiolek, math.DG/0702196 (2007), Proc. Steklov Math. Inst., vol. 259, 73-81 (pdf)

44. Pseudodifferential symbols on Riemann surfaces and Krichever-Novikov algebras. with Dmitry Donin, Comm. Math. Phys., 272:2 (2007), 507-527; DOI 10.1007/s00220-007-0234-2.

43. Topological fluid dynamics. Notices of the AMS, 52:1 (2005), 9-19; (pdf ).

42. Polar linkings, intersections, and Weil pairing. with Alexei Rosly, Proc. of Royal Soc. London A, 461 (2005), 3505-3524 (pdf).

41. Asymptotic directions, Monge-Ampere equations and the geometry of diffeomorphism groups. with Gerard Misiolek, Journal of Math. Fluid Mech. 7 (2005), S365-S375; (math.DG/0504556, pdf).

40. A polar de Rham theorem. with Alexei Rosly and Richard Thomas, Topology 43 (2004), 1231-1246; (math.AG/0305081, pdf).

39. Bihamiltonian structures and quadratic algebras in hydrodynamics and on non-commutative torus. with Andrey Levin and Mikhail Olshanetsky, Comm. Math. Phys. 250 (2004), 581-612; (nlin.SI/0309017, pdf).

38. Comments to Arnold's Problems, in Arnold's Problems, Phasis, Moscow (2000), 454pp; Springer (2004), 639pp.

37. The flow completion of the Burgers equation. with Peter Michor, in Infinite-dimensional groups and manifolds: IRMA Lectures in Math. and Theor. Physics (Ed.: T.Wurzbacher), Walter de Gruyter & Co., Berlin, 2004, 17-27.

36. Geometry of fluid motion. Séminaire Équat. Dér. Part., Ecole Polytechnique X (2003), 1-10

35. Euler equations on homogeneous spaces and Virasoro orbits. with Gerard Misiolek, Advances in Math. 176 (2003), 116-144; (pdf).

34. Geometry of higher helicities. Moscow Math. Journal 3:3 (2003), 989-1011.

33. Polar homology. with Alexei Rosly, Canad. J. Math. 55 (2003), 1100-1120; (pdf).

32. A Poisson--Lie framework for rational reductions of the KP hierarchy. Letters in Math. Physics 58 (2001), 101-107; (pdf).

31. Polar homology and holomorphic bundles. with Alexei Rosly, Phil. Trans. Royal Soc. London A 359 (2001), 1413-1427; (pdf).

30. Topology bounds the energy. An Introduction to the Geometry and Topology of Fluid Flows (Ed.: R.L. Ricca), Kluwer, Dordrecht, The Netherlands (2001), 229-238.

29. Symplectic geometry on moduli spaces of holomorphic bundles over complex surfaces. with Alexei Rosly, The Arnoldfest (Eds.: E.Bierstone et al.), Fields Institute Communications 24 (1999), 311-323.

28. Homotopy classification of nondegenerate quasiperiodic curves on the $2$-sphere. (with B.Shapiro) Publ. Inst. Math. (Beograd) (N.S.), 66(80) (1999), 127--156.

27. Extensions and contractions of the Lie algebra of q-pseudodifferential symbols on the circle. with Volodymyr Lyubashenko and Claude Roger, J. of Funct. Anal. 143:1 (1997), 55-97; (pdf).

26. Informal complexification and Poisson structures on moduli spaces. AMS Transl., Ser. 2, 180 (1997), 147-155.

25. Four-dimensional realization of two-dimensional current groups. with Igor Frenkel, Comm. Math. Phys. 178 (1996), 541-562.

24. Universal Drinfeld-Sokolov reduction and matrices of complex size. with Feodor Malikov, Comm. Math. Phys. 175 (1996), 113-134.

23. On cohomology of the Lie algebra of pseudodifferential symbols on a circle. with Claude Roger, J. Math. Sci. 82:6 (1996), 3800--3806.

22. The Lie-Poisson group of pseudodifferential symbols. with Ilya Zakharevich, Comm. Math. Phys. 171 (1995), 475-530.

21. Affine Gelfand-Dickey brackets and holomorphic vector bundles. with Pavel Etingof, Geom. and Funct. Anal. 4 (1994), 399-423.

20. Steady fluid flows and symplectic geometry. with Viktor Ginzburg, J. of Geometry and Physics 14 (1994), 195-210.

19. The Lie-Poisson group of pseudodifferential symbols and fractional KP-KdV-hierarchies. (with I.Zakharevich) C.R. Acad. Sci. Paris, 316 (1993), Serie I, 621-626.

18. The logarithm of the derivative operator and higher spin algebras of $W_{\infty}$-type. (with I.Bakas and E.Kiritsis) Comm. Math. Phys., 151 (1993), 233-243.

17. Topological methods in hydrodynamics. (with V.Arnold) Annual Reviews in Fluid Mechanics, 24 (1992), 145-166.

16. Ergodic interpretation of integral hydrodynamic invariants. J. of Geometry and Physics, 9 (1992), 101-110.

15. A hierarchy of centrally extended algebras and the logarithm of the derivative operator. Int. Math. Research Notices (Duke Math. J.), 1:1 (1992), 1-5.

14. Topology of steady fluid flows. (with V.Ginzburg) Topological Aspects of the Dynamics of Fluid and Plasmas, eds. H.K.Moffatt, G.M.Zaslavsky, P.Comte, M.Tabor (Kluwer Acad. Publ.), (1992), 265-272.

13. Swallowtails and Whitney umbrellas are homeomorphic. (with B. Shapiro) J. of Alg. Geometry, 1 (1992), 549-560.

12. Non-degenerate curves on $S^2$ and orbit classification of the Zamolodchikov algebra. (with B. Shapiro) Comm. Math. Phys., 145:2 (1992), 357-362.

11. Central extension of the algebra of pseudodifferential symbols.(with O. Kravchenko) Funct. Anal. Appl., 25:2 (1991), 152-154.

10. Singularities of light hypersurfaces and the structure of hyperbolicity sets for systems of partial differential equations. Advances in Soviet Mathematics, AMS, ed. V.I.Arnold, 1 (1990), 105-118.

9. Symplectic leaves of the Gelfand-Dikii brackets and homotopy classes of non-degenerate curves.(with V. Ovsienko) Funct. Anal. Appl., 24:1 (1990), 33-40.

8. Invariants of Hamiltonian KdV-structures. Russ. Math. Surveys, 45:1 (1990), 209-210.

7. Versal deformations of intersections of invariant submanifolds of dynamical systems. Russ. Math. Surveys, 44:3 (1989), 181-182.

6. Invariants of the Euler equations for ideal or barotropic hydrodynamics and superconductivity in D dimensions. with Yuri Chekanov, Physica D 40:1 (1989), 119-131.

5. Integrals of motion of the Euler equation of multidimensional hydrodynamics and superconductivity.(with Yu.Chekanov and V.Ovsienko) Diff.Geom., Lie Groups and Mechanics, Zap. Sem. LOMI, 172 (1988), 105-113 (in Russian). English transl.: J. of Sov. Math., 59:5 (1992), 1096-1102.

4. Bifurcations of gradient dynamical systems. Modern Problems in Math., New Achievements, VINITI AN USSR, 33 (1988), 113-155 (in Russian). English transl.: J. of Sov. Math. 52 (1990), 3279-3305.

3. The (super) Korteweg-de Vries equation as an Euler equation. with Valentin Ovsienko, Funktsional. Anal. i Prilozhen. 21:4 (1987), 81--82; English transl: Funct. Anal. and Appl. 21:4 (1987), 329-331.

2. Homogeneous vector fields and Whitney umbrellas. Russ. Math. Surveys, 42:5 (1987), 171-172.

1. Bifurcations of singular points of gradient vector fields. Funct. Anal. Appl., 20:3 (1986), 250-252.


Books/volumes/papers edited

13E. Vladimir I. Arnold. Collected Works. Editors: A.Givental, B.Khesin, M.Sevryuk et al. Volume VI: Dynamics, combinatorics, and invariants of knots, curves, and wave fronts, 1992-1995; Springer-Nature (2023), 491pp.

12B. Special Volume of Celebratio Mathematica on Dmitry Fuchs. Editors: B.Khesin, F.Malikov, V.Ovsienko, and S.Tabachnikov, celebratio.org (2022), 150pp.

11B. Special Issue in honour of Alexander Shnirelman's 75th birthday. Editors: D.Jakobson, B.Khesin, and I.Polterovich, Annales mathématiques du Québec}, 46:1 (2022), 225pp.

10E. Algebra, Topology, and Dynamics in Interaction. Editors: B.Khesin, F.Malikov, V.Ovsienko, S.Tabachnikov, SIGMA Journal: Volume in honor of D.Fuchs' 80th anniversary, (2020), 252pp.

9E. Vladimir I. Arnold. Collected Works. Editors: A.Givental, B.Khesin, M.Sevryuk et al. Volume IV: Singularities in symplectic and contact geometry, 1980-1985; Springer (2018), 541pp.

8E. Vladimir I. Arnold. Collected Works. Editors: A.Givental, B.Khesin, M.Sevryuk et al. Volume III: Singularity theory, 1972-1979; Springer (2016), 509pp.

7E. ARNOLD: Swimming Against the Tide. Editors: B.Khesin and S.Tabachnikov, AMS (2014), 224pp.

6E. Vladimir I. Arnold. Collected Works. Editors: A.Givental, B.Khesin, A.Varchenko et al. Volume II: Hydrodynamics, bifurcation theory, and algebraic geometry, 1965-1972; Springer (2014), 466pp.

4-5E. Tribute to Vladimir Arnold; Memories of Vladimir Arnold. (coord. eds. with Serge Tabachnikov), Notices of the AMS 59, March and April (2012), 378-399 and 482-502.

3E. Vladimir I. Arnold. Collected Works. Editors: A.Givental, B.Khesin, J.Marsden, A.Varchenko et al. Volume I: Representation of functions, Celestial mechanics, and KAM theory, 1957-1965; Springer (2009), 487pp.

2E. Symplectic and contact topology: Interactions and perspectives. Editors: Ya.Eliashberg, B.Khesin, and F.Lalonde, Fields Institute Communications, v.35, AMS, Providence (2003), 201pp.

1E. The Arnoldfest: Proceedings of a conference in honour of V.I.Arnold for his sixtieth birthday, Toronto (1997), Editors: E.Bierstone, B.Khesin, A.Khovanskii, and J.Marsden, Fields Institute Communications, v.24, AMS, Providence (1999), 556pp.