Tadahiro (Choonghong) Oh
  • Professor
    • Mailing Address:
    School of Mathematics
    The University of Edinburgh
    James Clerk Maxwell Building, Rm 4609
    The King's Buildings, Peter Guthrie Tait Road
    Edinburgh, EH9 3FD, United Kingdom

    Office: Rm 4609 JCMB
    e-mail: hiro.oh ed.ac.uk
        duck or rabbit?
        Oct. 2007
    Also, niece & nephew, Aug. 2014
    Mar. 2013, Oct. 2012, Dec. 2011
    Research | Brief CV | Selected Papers | Papers | Notes | Talks | Ph.D. students | Teaching | Links
    My old VF friend, Tetsuo Shimizu, from NYC. If you see this, please contact me!! I tried to look for you for decades but could not find you.

    Want to learn how to count? Cute movie on "Combinatorial Explosion" by National Museum of Emerging Science and Innovation in Japan

    Advice from Michael Wymess on grant application

    Teaching:   Staff mail at UoE   Academic Calendar   Math intranet site   EASE   Learn   Pure   PATH
       
                                 
     Fall 24/Spring 25: Dispersive PDEs from the deterministic and probabilistic viewpoints (Ph.D. course): Course webpage
     Fall 24/Spring 25: Reading course on rough paths (Ph.D. course)
     Spring 22:   Stochastic PDEs with multiplicative noises (advanced Ph.D. course): Course webpage
     Fall 21:   Reading course on "Nonlinear Schrödinger Equations'' (MATH11114)
     Spring 21:   Singular stochastic dispersive PDEs (MIGSAA advanced Ph.D. course): Course webpage
     Spring 20:   Nonlinear Schrödinger Equations (MATH11137): course note
    Rough path theory and pathwise well-posedness of stochastic PDEs (MIGSAA advanced Ph.D. course): Course webpage
     Spring 19:   Two-dimensional statistical hydrodynamics (MIGSAA advanced Ph.D. course): Course webpage
     Spring 18:   Nonlinear Schrödinger Equations (MATH11137), Dispersive Equations (MIGSAA advanced Ph.D. course): Course webpage
    tutorials for Fundamentals of Pure Mathematics (FPM, MATH08064)
     Fall 17:   tutorials for Honours Differential Equations (HDEq, MATH10066)
     Spring 17:
          		Probabilistic Perspectives in Nonlinear Dispersive PDEs (MIGSAA advanced Ph.D. course): Course webpage
    tutorials for Fundamentals of Pure Mathematics (FPM, MATH08064)
     Fall 16:   tutorials for Honours Differential Equations (HDEq, MATH10066, 2 sections)
     Spring 16:
          		Nonlinear Schrödinger Equations (MATH11137), Dispersive Equations (MIGSAA advanced Ph.D. course): Course webpage
    tutorials for Fundamentals of Pure Mathematics (FPM, MATH08064, 2 sections)
     Fall 14: Introduction to Linear Algebra (ILA, MATH08057)
    tutorials for ILA (3 sections), Facets of Mathematics (MATH08068)
     Spring 14: tutorials for Proofs and Problem Solving (PPS, MATH08059, two-hour tutorial), Fourier Analysis (MATH10058), Honours Analysis (MATH10068, one-hour tutorial + two-hour Skills workshop)
     Fall 13:tutorials for Introduction to Linear Algebra (ILA, MATH08057, 2 sections), Accelerated Proofs and Problem Solving (APPS, MATH08071), Hilbert spaces (MATH10046)
    Research Interest:   Analysis group at UoE
    Nonlinear Partial Differential Equations and Harmonic Analysis. In particular, study of (deterministic and stochastic) nonlinear dispersive Hamiltonian PDEs, using the techniques from PDEs, nonlinear Fourier analysis, and probability. Mainly, short and long time behavior of solutions such as well-posedness (existence, uniqueness, and stability of solutions) in both deterministic and probabilistic settings, existence of invariant measures and their properties, solitons, growth of higher Sobolev norms related to weak turbulence, etc. Also, interested in multilinear integral/pseudodifferential operators.
    Seminars:   Analysis Seminar,   HWU Analysis Seminar,   NBPS,   UoE seminars,   UoE calendar   MI events,   ICMS events,   London Analysis and Probability Seminar,   Paris-London Analysis Seminar

    Selected Papers:

    Papers:

    • For published papers, please obtain copies from corresponding journals; see MathSciNet (old version) for the published papers. Preprints on arXiv may not be up-to-date.

    • For recent open access papers, there are links to both the published and arXiv versions.

    1. ♣ ♠ (with Y. Zine) Hyperbolic sine-Gordon model beyond the first threshold.
    2. ♣ ♠ (with A. Chapouto, J. Li) Fourier restriction norm method adapted to controlled paths.
    3. ♣ ♠ (with D. Greco, L. Tao, L. Tolomeo) Critical threshold for weakly interacting log-correlated focusing Gibbs measures.
    4. ♣ ♠ (with Á. Bényi, R.H. Torres) Symbolic calculus for a class of pseudodifferential operators with applications to compactness,
    5. ♣ ♠ (with M. Gubinelli, M. Hairer, Y. Zine) A simple construction of the sine-Gordon model via stochastic quantization.
    6. ♣ ♠ (with K. Chouk, M. Gubinelli, G. Li, J. Li) Nonlinear PDEs with modulated dispersion II: Korteweg-de Vries equation.
    7. ♠ (with A. Chapouto, G. Li) Deep-water and shallow-water limits of statistical equilibria for the intermediate long wave equation.
    8. ♠ (with Á. Bényi, G. Li, R.H. Torres) Compact T(1) theorem à la Stein.
    9. ♠ (with Á. Bényi, G. Li, R.H. Torres) Compact bilinear operators and paraproducts revisited (arXiv link), Canad. Math. Bull. 68 (2025), no. 1, 44--59.
    10. ♠ (with A. Chapouto, J. Forlano, G. Li, D. Pilod) Intermediate long wave equation in negative Sobolev spaces (arXiv link), Proc. Amer. Math. Soc. Ser. B 11 (2024), 452--468.
    11. ♠ (with Á. Bényi, T. Zhao) Fractional Leibniz rule on the torus, Proc. Amer. Math. Soc. 153 (2025), no. 1, 207--221.
    12. ♠ (with A. Chapouto, G. Li, D. Pilod) Deep-water limit of the intermediate long wave equation in L2, Math. Res. Lett. 31 (2024), no. 6, 1655--1692.
    13. ♠ (with J. Huang, M. Okamoto) On the local linearization of the one-dimensional stochastic wave equation with a multiplicative space-time white noise forcing (arXiv link), Proc. Amer. Math. Soc. Ser. B 11 (2024), 378--389.
    14. ♠ (with M. Okamoto, O. Pocovnicu, N. Tzvetkov) A remark on randomization of a general function of negative regularity (arXiv link), Proc. Amer. Math. Soc. Ser. B 11 (2024), 538--554.
    15. ♦ ♠ (with J. Quastel, P. Sosoe) Global dynamics for the stochastic KdV equation with white noise as initial data (arXiv link), Trans. Amer. Math. Soc. Ser. B 11 (2024), 420--460.
    16. ♠ (with L. Tolomeo, Y. Wang, G. Zheng) Hyperbolic P(Φ)2-model on the plane.
    17. ♠ (with G. Li, G. Zheng) On the deep-water and shallow-water limits of the intermediate long wave equation from a statistical viewpoint, to appear in Trans. London Math. Soc.
    18. ♠ (with I. Chevyrev, Y. Wang) Norm inflation for the cubic nonlinear heat equation above the scaling critical regularity, to appear in Funkcial. Ekvac.
    19. ♠ (with Á. Bényi) Discrete bilinear operators and commutators, J. Geom. Anal. 33 (2023), no. 3, Paper No. 102, 16pp.
    20. ♠ (with R. Liu) Sharp local well-posedness of the two-dimensional periodic nonlinear Schrödinger equation with a quadratic nonlinearity |u|2, Math. Res. Lett. 31 (2024), no. 1, 255--277.
    21. ♠ (with Y. Zine) A note on products of stochastic objects, to appear in Kyoto J. Math.
    22. ♠ (with R. Liu) On the two-dimensional singular stochastic viscous nonlinear wave equations, C. R. Math. Acad. Sci. Paris 360 (2022), 1227--1248.
    23. ♠ (with S. Čanić, J. Kuan) Probabilistic global well-posedness of a viscous nonlinear wave equation modeling fluid-structure interaction, Appl. Anal. 101 (2022), no.12, 4349--4373.
    24. ♠ (with Y. Wang, Y. Zine) Three-dimensional stochastic cubic nonlinear wave equation with almost space-time white noise (arXiv link), Stoch. Partial Differ. Equ. Anal. Comput. 10 (2022), 898--963. Special issue dedicated to Professor István Gyöngy on the occasion of his seventieth birthday.
    25. ♦ ♠ (with M. Okamoto, L. Tolomeo) Stochastic quantization of the Φ 3 3 -model (arXiv link), Memoirs of the European Mathematical Society, 16. European Mathematical Society (EMS), Berlin, 2025.
    26. ♠ (with K. Seong, L. Tolomeo) A remark on Gibbs measures with log-correlated Gaussian fields (arXiv link), Forum Math. Sigma 12 (2024), e50, 40 pp.
    27. ♠ (with K. Seong) Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation in negative Sobolev spaces, J. Funct. Anal. 281 (2021), no. 9, 109150, 49 pp.
    28. ♦ ♠ (with M. Okamoto, L. Tolomeo) Focusing Φ 4 3 -model with a Hartree-type nonlinearity, Mem. Amer. Math. Soc. 304 (2024), no. 1529.
    29. ♦ ♠ (with T. Robert, N. Tzvetkov, Y. Wang) Stochastic quantization of Liouville conformal field theory.
    30. ♦ ♠ (with T. Robert, P. Sosoe, Y. Wang) Invariant Gibbs dynamics for the dynamical sine-Gordon model, Proc. Roy. Soc. Edinburgh Sect. A 151 (2021), no. 5, 1450--1466.
    31. ♦ ♠ (with T. Robert, Y. Wang) On the parabolic and hyperbolic Liouville equations (arXiv link), Comm. Math. Phys. 387 (2021), no. 3 1281--1351.
    32. ♦ ♠ (with M. Okamoto) Comparing the stochastic nonlinear wave and heat equations: a case study (arXiv link), Electron. J. Probab. 26 (2021), Paper No. 9, 44 pp.
    33. ♦ ♠ (with K. Cheung, G. Li) Almost conservation laws for stochastic nonlinear Schrödinger equations (arXiv link), J. Evol. Equ. 21 (2021), 1865--1894.
    34. ♦ (with T. Robert, P. Sosoe, Y. Wang) On the two-dimensional hyperbolic stochastic sine-Gordon equation (arXiv link), Stoch. Partial Differ. Equ. Anal. Comput. 9 (2021), 1--32.
    35. ♦ ♠ (with M. Gubinelli, H. Koch, L. Tolomeo) Global dynamics for the two-dimensional stochastic nonlinear wave equations (arXiv link), Int. Math. Res. Not. 2022, no. 21, 16954--16999.
    36. ♦ ♠ (with M. Okamoto, T. Robert) A remark on triviality for the two-dimensional stochastic nonlinear wave equation (arXiv link), Stochastic Process. Appl. 130 (2020), no. 9, 5838--5864.
    37. ♦ (with M. Okamoto) On the stochastic nonlinear Schrödinger equations at critical regularities (arXiv link), Stoch. Partial Differ. Equ. Anal. Comput. 8 (2020), no. 4, 869--894.
    38. ♦ ♠ (with J. Forlano) Normal form approach to the one-dimensional cubic nonlinear Schrödinger equation in Fourier-amalgam spaces.
    39. ♦ ♠ (with A. Chapouto, K. Cheung) Global well-posedness of the periodic stochastic KdV equation with multiplicative noise.
    40. ♦ ♠ (with O. Pocovnicu, N. Tzvetkov) Probabilistic local Cauchy theory of the cubic nonlinear wave equation in negative Sobolev spaces (arXiv link), Ann. Inst. Fourier (Grenoble) 72 (2022) no. 2, 771--830.
    41. ♦ ♠ (with T. Robert, N. Tzvetkov) Stochastic nonlinear wave dynamics on compact surfaces (arXiv link), Ann. H. Lebesgue 6 (2023), 161--223.
    42. ♦ ♠ (with P. Sosoe, L. Tolomeo) Optimal integrability threshold for Gibbs measures associated with focusing NLS on the torus (arXiv link), Invent. Math. 227 (2022), no. 3, 1323--1429.
    43. ♦ ♠ (with T. Gunaratnam, N. Tzvetkov, H. Weber) Quasi-invariant Gaussian measures for the nonlinear wave equation in three dimensions, Probab. Math. Phys. 3 (2022), no. 2, 343--379.
    44. ♦ ♠ (with M. Okamoto, N. Tzvetkov) Uniqueness and non-uniqueness of the Gaussian free field evolution under the two-dimensional Wick ordered cubic wave equation (arXiv link), Ann. Inst. Henri Poincaré Probab. Stat. 60 (2024), no. 3, 1684--1728.
    45. ♦ ♠ (with M. Gubinelli, H. Koch) Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity (arXiv link), J. Eur. Math. Soc. 26 (2024), no. 3, 817--874.
    46. ♦ ♠ (with Y. Wang) On global well-posedness of the modified KdV equation in modulation spaces (arXiv link), Discrete Contin. Dyn. Syst. A 41 (2021), no. 6, 2971--2992.
    47. ♦ (with Y. Wang) Normal form approach to the one-dimensional periodic cubic nonlinear Schrödinger equation in almost critical Fourier-Lebesgue spaces (arXiv), J. Anal. Math. 143 (2021), no. 2, 723--762.
    48. ♦ (with Y. Wang) Global well-posedness of the one-dimensional cubic nonlinear Schrödinger equation in almost critical spaces, J. Differential Equations 269 (2020), no. 1, 612--640.
    49. ♦ (with Á. Bényi) Modulation spaces with scaling symmetry, Appl. Comput. Harmon. Anal. 48 (2020), no.1, 496--507.
    50. ♦ (with J. Forlano, Y. Wang) Stochastic cubic nonlinear Schrödinger equation with almost space-time white noise, J. Aust. Math. Soc. 109 (2020), no. 1, 44--67.
    51. ♦ (with O. Pocovnicu, Y. Wang) On the stochastic nonlinear Schrödinger equations with non-smooth additive noise, Kyoto J. Math. 60 (2020), no. 4, 1227--1243.
    52. ♦ (with S. Kwon, H. Yoon) Normal form approach to unconditional well-posedness of nonlinear dispersive PDEs on the real line, Ann. Fac. Sci. Toulouse Math. 29 (2020), no. 3, 649--720.
    53. ♦ (with Á. Bényi, O. Pocovnicu) On the probabilistic Cauchy theory for nonlinear dispersive PDEs, Landscapes of Time-Frequency Analysis. 1--32, Appl. Numer. Harmon. Anal., Birkhäuser/Springer, Cham, 2019.
    54. ♦ (with Y. Tsutsumi, N. Tzvetkov) Quasi-invariant Gaussian measures for the cubic nonlinear Schrödinger equation with third order dispersion, C. R. Math. Acad. Sci. Paris 357 (2019), no. 4, 366--381.
    55. ♦ (with Á. Bényi, O. Pocovnicu) Higher order expansions for the probabilistic local Cauchy theory of the cubic nonlinear Schrödinger equation on ℝ3 (arXiv link), Trans. Amer. Math. Soc. Ser. B 6 (2019), 114--160.
    56. ♦ ♠ (with N. Tzvetkov, Y. Wang) Solving the 4NLS with white noise initial data (arXiv link), Forum Math. Sigma 8 (2020), e48, 63 pp.
    57. ♦ (with M. Okamoto, O. Pocovnicu) On the probabilistic well-posedness of the nonlinear Schrödinger equations with non-algebraic nonlinearities (arXiv link), Discrete Contin. Dyn. Syst. A. 39 (2019), no. 6, 3479--3520.
    58. ♦ (with N. Tzvetkov) Quasi-invariant Gaussian measures for the two-dimensional defocusing cubic nonlinear wave equation, J. Eur. Math. Soc. 22 (2020), no. 6, 1785--1826.
    59. ♦ (with Y. Wang) Global well-posedness of the periodic cubic fourth order NLS in negative Sobolev spaces (arXiv link), Forum Math. Sigma 6 (2018), e5, 80 pp.
    60. ♦ (with L. Thomann) Invariant Gibbs measures for the 2-d defocusing nonlinear wave equations, Ann. Fac. Sci. Toulouse Math. 29 (2020), no. 1, 1--26.
    61. ♦ (with M. Gubinelli, H. Koch) Renormalization of the two-dimensional stochastic nonlinear wave equations, Trans. Amer. Math. Soc. 370 (2018), no 10, 7335--7359.
    62. ♦ (with P. Sosoe, N. Tzvetkov) An optimal regularity result on the quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation (arXiv link), J. Éc. polytech. Math. 5 (2018), 793--841.
    63. ♦ (with N. Tzvetkov) On the transport of Gaussian measures under the flow of Hamiltonian PDEs, Séminaire Laurent Schwartz--Équations aux dérivées partielles et applications. Année 2015--2016, Exp. No. VI, 9 pp., Ed. Éc. Polytech., Palaiseau, 2017.
    64. ♦ A remark on norm inflation with general initial data for the cubic nonlinear Schrödinger equations in negative Sobolev spaces, Funkcial. Ekvac. 60 (2017) 259--277.
    65. ♦ (with G. Richards, L. Thomann) On invariant Gibbs measures for the generalized KdV equations, Dyn. Partial Differ. Equ. 13 (2016), no. 2, 133--153.
    66. ♦ (with Y. Wang) On the ill-posedness of the cubic nonlinear Schrödinger equation on the circle, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 64 (2018), no. 1, 53--84.
    67. ♦ (with J. Chung, Z. Guo, S. Kwon) Normal form approach to global well-posedness of the quadratic derivative nonlinear Schrödinger equation on the circle, Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), 1273--1297.
    68. ♦ (with N. Tzvetkov) Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation (arXiv link), Probab. Theory Related Fields 169 (2017), 1121--1168.
    69. ♦ (with O. Pocovnicu) A remark on almost sure global well-posedness of the energy-critical defocusing nonlinear wave equations in the periodic setting, Tohoku Math. J. 69 (2017), no.3, 455--481.
    70. ♦ (with L. Thomann) A pedestrian approach to the invariant Gibbs measures for the 2-d defocusing nonlinear Schrödinger equations (arXiv link), Stoch. Partial Differ. Equ. Anal. Comput. 6 (2018), 397--445.
    71. ♦ (with O. Pocovnicu) Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on ℝ3, J. Math. Pures Appl. 105 (2016), 342--366.
    72. (with R. Mosincat) A remark on global well-posedness of the derivative nonlinear Schrödinger equation on the circle, C. R. Math. Acad. Sci. Paris. 353 (2015), no. 9, 837--841.
    73. (with Á. Bényi) Linear and bilinear T(b) theorems à la Stein (arXiv link), Proc. Amer. Math. Soc. Ser. B 2 (2015), 1--16.
    74. ♦ (with Z. Guo) Non-existence of solutions for the periodic cubic nonlinear Schrödinger equation below L2, Int. Math. Res. Not. 2018, no. 6, 1656--1729.
    75. Global existence for the defocusing nonlinear Schrödinger equations with limit periodic initial data, Commun. Pure Appl. Anal. 14 (2015), no. 4, 1563--1580. Special issue dedicated to Professor Gustavo Ponce on the occasion of his sixtieth birthday.
    76. ♦ ♠ (with J. Quastel, P. Sosoe) Invariant Gibbs measures for the defocusing nonlinear Schrödinger equations on the real line.
    77. On nonlinear Schrödinger equations with almost periodic initial data, SIAM J. Math. Anal. 47 (2015), no. 2, 1253--1270.
    78. ♦ (with Á. Bényi, O. Pocovnicu) On the probabilistic Cauchy theory of the cubic nonlinear Schrödinger equation on ℝd, d ≥ 3 (arXiv link), Trans. Amer. Math. Soc. Ser. B 2 (2015), 1--50.
    79. (with Á. Bényi, O. Pocovnicu) Wiener randomization on unbounded domains and an application to almost sure well-posedness of NLS, Excursions in harmonic analysis. Vol. 4, 3--25, Appl. Numer. Harmon. Anal., Birkhäuser/Springer, Cham, 2015.
    80. (with Z. Guo, Y. Wang) Strichartz estimates for Schrödinger equations on irrational tori, Proc. Lond. Math. Soc. 109 (2014), no. 4, 975--1013.
    81. (with Á. Bényi) Smoothing of commutators for a Hörmander class of bilinear pseudodifferential operators, J. Fourier Anal. Appl. 20 (2014), no. 2, 282--300.
    82. (with J. Quastel) On Cameron-Martin theorem and almost sure global existence, Proc. Edinb. Math. Soc. 59 (2016), 483--501.
    83. ♦ (with R. Killip, O. Pocovnicu, M. Vişan) Solitons and scattering for the cubic-quintic nonlinear Schrödinger equation on ℝ3, Arch. Ration. Mech. Anal. 225 (2017), no. 1, 469--548.
    84. (with Á. Bényi) On a class of bilinear pseudodifferential operators, J. Funct. Spaces Appl. vol. 2013, Article ID 560976, 5 pp, 2013. doi:10.1155/2013/560976.
    85. (with J. Colliander, J. Marzuola, G. Simpson) Behavior of a model dynamical system with applications to weak turbulence, Exp. Math. 22 (2013), no. 3, 250--264.
    86. A blowup result for the periodic NLS without gauge invariance, C. R. Math. Acad. Sci. Paris 350 (2012), no. 7--8, 389--392.
    87. (with R. Killip, O. Pocovnicu, M. Vişan) Global well-posedness of the Gross-Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions, Math. Res. Lett. 19 (2012), no. 5, 969--986.
    88. (with Á. Bényi) The Sobolev inequality on the torus revisited, Publ. Math. Debrecen 83 (2013), no. 3, 359--374.
    89. (with Z. Guo, S. Kwon) Poincaré-Dulac normal form reduction for unconditional well-posedness of the periodic cubic NLS, Comm. Math. Phys. 322 (2013), no.1, 19--48.
    90. (with J. Quastel) On invariant Gibbs measures conditioned on mass and momentum, J. Math. Soc. Japan 65 (2013), no. 1, 13--35.
    91. (with J. Colliander, S. Kwon) A remark on normal forms and the "upside-down" I-method for periodic NLS: growth of higher Sobolev norms, J. Anal. Math. 118 (2012), 55--82.
    92. (with A. Nahmod, L. Rey-Bellet, G. Staffilani) Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS, J. Eur. Math. Soc. 14 (2012), 1275--1330.
    93. (with S. Kwon) On unconditional well-posedness of modified KdV, Int. Math. Res. Not. 2012, no. 15, 3509--3534.
    94. (with C. Sulem) On the one-dimensional cubic nonlinear Schrödinger equation below L2, Kyoto J. Math. 52 (2012), no.1, 99--115.
    95. (with Á. Bényi) Modulation spaces, Wiener amalgam spaces, and Brownian motions, Adv. Math. 228 (2011), no. 5, 2943--2981.
    96. Remarks on nonlinear smoothing under randomization for the periodic KdV and the cubic Szegö equation, Funkcial. Ekvac. 54 (2011), no. 3, 335--365.
    97. White noise for KdV and mKdV on the circle, Harmonic analysis and nonlinear partial differential equations, 99--124, RIMS Kôkyûroku Bessatsu, B18, Res. Inst. Math. Sci. (RIMS), Kyoto, 2010.
    98. (with J. Quastel, B. Valkó) Interpolation of Gibbs measures and white noise for Hamiltonian PDE, J. Math. Pures Appl. 97 (2012), no. 4, 391--410.
    99. (with J. Colliander) Almost sure well-posedness of the cubic nonlinear Schrödinger equation below L2(𝕋), Duke Math. J. 161 (2012), no. 3, 367--414.
    100. Periodic stochastic Korteweg-de Vries equation with additive space-time white noise, Anal. PDE 2 (2009), no. 3, 281--304.
    101. Invariance of the white noise for KdV, Comm. Math. Phys. 292 (2009), no. 1, 217--236. Also, see Erratum: Invariance of the white noise for KdV, in preparation. For the correct nonlinear analysis, please see ''White noise for KdV and mKdV on the circle''.
    102. Invariance of the Gibbs measure for the Schrödinger-Benjamin-Ono system, SIAM J. Math. Anal. 41 (2009/10), no. 6, 2207--2225.
    103. Invariant Gibbs measures and a.s. global well-posedness for coupled KdV systems, Differential Integral Equations 22 (2009), no. 7--8, 637--668.
    104. Diophantine conditions in global well-posedness of coupled KdV-type systems, Electron. J. Differential Equations 2009, no. 52, 48 pp.
    105. Diophantine conditions in well-posedness theory of coupled KdV-type systems: local theory, Int. Math. Res. Not. 2009, no. 18, 3516--3556.
    106. (with Á. Bényi) Best Constants for Certain Multilinear Integral Operators, J. Inequal. Appl. 2006, Art. ID 28582, 12 pp.
    Book: Notes (see also course notes under teaching):

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