• 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.

• ♣ = papers supported by my EPSRC mathematical sciences small grant (2024-2025).
• ♠  = papers supported by my ERC Consolidator Grant "SingStocDispDyn" (2020-2026). See HERE for papers by other group members (partially) supported under this grant.
• ♦  = papers supported by my ERC Starting Grant "ProbDynDispEq" (2015-2020). See HERE for papers by other group members (partially) supported under this grant.

1. ♠ (with L. Tolomeo, N. Tzvetkov, Y. Wang) Non-triviality of the radial Φ⁴-model in the energy critical and supercritical regimes.
2. ♣ ♠ (with A. Chapouto, J. Forlano) Normal form integrator for dispersive equations.
3. ♣ ♠ (with D. Greco, P. Sosoe, Y. Wang) Unconditional well-posedness of the stochastic Korteweg-de Vries equation with an additive noise.
4. ♠ (with G. Li, J. Li, S. Liu, and N. Tzvetkov) Probabilistic well-posedness of dispersive PDEs beyond variance blowup II: quadratic nonlinear wave equation.
5. ♠ (with Y. Shao) Sewing lemma approach to the 1-d periodic cubic nonlinear Schrödinger equation I.
6. ♣ ♠ (with A. Chapouto, J. Li, M. Okamoto) Pathwise local well-posedness of the stochastic Korteweg-de Vries equation with a multiplicative Young noise.
7. ♠ (with A. Chapouto, B. Harrop-Griffiths, G. Li) On the singular nature of shallow-water convergence of the intermediate long wave equation on the real line.
8. ♣ ♠ (with D. Greco, M. Gubinelli, S. Liu) Refined global well-posedness for the periodic modulated Korteweg-de Vries equation.
9. ♣ ♠ (with A. Chapouto, J. Li) Fourier restriction norm method adapted to controlled paths: stochastic wave equations.
10. ♠ (with A. Chapouto, G. Li, T. Zhao) Shallow-water convergence of the intermediate long wave equation in L².
11. ♣ ♠ (with R. Liu, S. Liu) Hyperbolic O(N) linear sigma model and its mean-field limit.
12. ♣ ♠ (with G. Li, J. Li, and N. Tzvetkov) Probabilistic well-posedness of dispersive PDEs beyond variance blowup I: Benjamin-Bona-Mahony equation.
13. ♣ ♠ (With E. Başakoğlu, Y. Wang) Sharp unconditional well-posedness of the 2-d periodic cubic hyperbolic nonlinear Schrödinger equation.
14. ♣ ♠ (with D. Greco, G. Li, R. Liang, Y. Wang) Optimal divergence rate of the focusing Gibbs measures.
15. ♣ ♠ (with M. Gubinelli, G. Li, J. Li) Nonlinear PDEs with modulated dispersion IV: normal form approach and unconditional uniqueness, to appear in Peking Math. J.
16. ♣ ♠ (with A. Chapouto, M. Gubinelli, G. Li, J. Li) Nonlinear PDEs with modulated dispersion III: multiplicative noises.
17. ♣ ♠ (with Y. Wang) Revisiting Bourgain's probabilistic construction of solutions to the 2-d cubic NLS,
18. ♣ ♠ (with D. Greco, L. Tao, L. Tolomeo) Critical threshold for weakly interacting log-correlated focusing Gibbs measures (arXiv link), Proc. Amer. Math. Soc. Ser. B 12 (2025), 150--165.
19. ♣ ♠ (with Á. Bényi, R.H. Torres) Symbolic calculus for a class of pseudodifferential operators with applications to compactness, J. Geom. Anal. 35 (2025), no. 10, Paper No. 301. Special issue dedicated to Professor Jill Pipher.
20. ♣ ♠ (with M. Gubinelli, M. Hairer, Y. Zine) A simple construction of the sine-Gordon model via stochastic quantization, J. Lond. Math. Soc. 112 (2025), no. 1, Paper No. e70214.
21. ♣ ♠ (with K. Chouk, M. Gubinelli, G. Li, J. Li) Nonlinear PDEs with modulated dispersion II: Korteweg-de Vries equation.
22. ♠ (with A. Chapouto, G. Li) Deep-water and shallow-water limits of statistical equilibria for the intermediate long wave equation.
23. ♠ (with Á. Bényi, G. Li, R.H. Torres) Compact T(1) theorem à la Stein, J. Funct. Anal. 289 (2025), no. 7, Paper No. 111052.
24. ♠ (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.
25. ♠ (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.
26. ♠ (with Á. Bényi, T. Zhao) Fractional Leibniz rule on the torus, Proc. Amer. Math. Soc. 153 (2025), no. 1, 207--221.
27. ♠ (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.
28. ♠ (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.
29. ♠ (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.
30. ♦ ♠ (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.
31. ♠ (with L. Tolomeo, Y. Wang, G. Zheng) Hyperbolic P(Φ)₂-model on the plane (arXiv link), Comm. Math. Phys. 407 (2026), no. 2, Paper No. 34.
32. ♠ (with G. Li, G. Zheng) On the deep-water and shallow-water limits of the intermediate long wave equation from a statistical viewpoint (arXiv link), Trans. London Math. Soc. 12 (2025), no. 1, Paper No. e70005.
33. ♠ (with I. Chevyrev, Y. Wang) Norm inflation for the cubic nonlinear heat equation above the scaling critical regularity, Funkcial. Ekvac. 68 (2025), no. 2, 145--164.
34. ♠ (with Á. Bényi) Discrete bilinear operators and commutators, J. Geom. Anal. 33 (2023), no. 3, Paper No. 102, 16pp.
35. ♠ (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.
36. ♠ (with Y. Zine) A note on products of stochastic objects, Kyoto J. Math. 65 (2025), no. 3, 637--668.
37. ♠ (with R. Liu) On the two-dimensional singular stochastic viscous nonlinear wave equations, C. R. Math. Acad. Sci. Paris 360 (2022), 1227--1248.
38. ♠ (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.
39. ♠ (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.
40. ♦ ♠ (with M. Okamoto, L. Tolomeo) Stochastic quantization of the Φ ³ ₃ -model (arXiv link), Mem. Eur. Math. Soc., 16. EMS Press, Berlin, 2025, viii+145 pp.
41. ♠ (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.
42. ♠ (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.
43. ♦ ♠ (with M. Okamoto, L. Tolomeo) Focusing Φ ⁴ ₃ -model with a Hartree-type nonlinearity, Mem. Amer. Math. Soc. 304 (2024), no. 1529, vi+143 pp.
44. ♦ ♠ (with T. Robert, N. Tzvetkov, Y. Wang) Stochastic quantization of Liouville conformal field theory.
45. ♦ ♠ (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.
46. ♦ ♠ (with T. Robert, Y. Wang) On the parabolic and hyperbolic Liouville equations (arXiv link), Comm. Math. Phys. 387 (2021), no. 3 1281--1351.
47. ♦ ♠ (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.
48. ♦ ♠ (with K. Cheung, G. Li) Almost conservation laws for stochastic nonlinear Schrödinger equations (arXiv link), J. Evol. Equ. 21 (2021), 1865--1894.
49. ♦ (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.
50. ♦ ♠ (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.
51. ♦ ♠ (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.
52. ♦ (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.
53. ♦ ♠ (with J. Forlano) Normal form approach to the one-dimensional cubic nonlinear Schrödinger equation in Fourier-amalgam spaces.
54. ♦ ♠ (with A. Chapouto, K. Cheung) Global well-posedness of the periodic stochastic KdV equation with multiplicative noise.
55. ♦ ♠ (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.
56. ♦ ♠ (with T. Robert, N. Tzvetkov) Stochastic nonlinear wave dynamics on compact surfaces (arXiv link), Ann. H. Lebesgue 6 (2023), 161--223.
57. ♦ ♠ (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.
58. ♦ ♠ (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.
59. ♦ ♠ (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.
60. ♦ ♠ (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.
61. ♦ ♠ (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.
62. ♦ (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.
63. ♦ (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.
64. ♦ (with Á. Bényi) Modulation spaces with scaling symmetry, Appl. Comput. Harmon. Anal. 48 (2020), no.1, 496--507.
65. ♦ (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.
66. ♦ (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.
67. ♦ (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.
68. ♦ (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.
69. ♦ (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.
70. ♦ (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.
71. ♦ ♠ (with N. Tzvetkov, Y. Wang) Solving the 4NLS with white noise initial data (arXiv link), Forum Math. Sigma 8 (2020), e48, 63 pp.
72. ♦ (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.
73. ♦ (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.
74. ♦ (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.
75. ♦ (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.
76. ♦ (with M. Gubinelli, H. Koch) Renormalization of the two-dimensional stochastic nonlinear wave equations, Trans. Amer. Math. Soc. 370 (2018), no 10, 7335--7359.
77. ♦ (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.
78. ♦ (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.
79. ♦ 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.
80. ♦ (with G. Richards, L. Thomann) On invariant Gibbs measures for the generalized KdV equations, Dyn. Partial Differ. Equ. 13 (2016), no. 2, 133--153.
81. ♦ (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.
82. ♦ (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.
83. ♦ (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.
84. ♦ (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.
85. ♦ (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.
86. ♦ (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.
87. (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.
88. (with Á. Bényi) Linear and bilinear T(b) theorems à la Stein (arXiv link), Proc. Amer. Math. Soc. Ser. B 2 (2015), 1--16.
89. ♦ (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.
90. 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.
91. ♦ ♠ (with J. Quastel, P. Sosoe) Invariant Gibbs measures for the defocusing nonlinear Schrödinger equations on the real line.
92. On nonlinear Schrödinger equations with almost periodic initial data, SIAM J. Math. Anal. 47 (2015), no. 2, 1253--1270.
93. ♦ (with Á. Bényi, O. Pocovnicu) On the probabilistic Cauchy theory of the cubic nonlinear Schrödinger equation on ℝ^d, d ≥ 3 (arXiv link), Trans. Amer. Math. Soc. Ser. B 2 (2015), 1--50.
94. (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.
95. (with Z. Guo, Y. Wang) Strichartz estimates for Schrödinger equations on irrational tori, Proc. Lond. Math. Soc. 109 (2014), no. 4, 975--1013.
96. (with Á. Bényi) Smoothing of commutators for a Hörmander class of bilinear pseudodifferential operators, J. Fourier Anal. Appl. 20 (2014), no. 2, 282--300.
97. (with J. Quastel) On Cameron-Martin theorem and almost sure global existence, Proc. Edinb. Math. Soc. 59 (2016), 483--501.
98. ♦ (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.
99. (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.
100. (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.
101. A blowup result for the periodic NLS without gauge invariance, C. R. Math. Acad. Sci. Paris 350 (2012), no. 7--8, 389--392.
102. (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.
103. (with Á. Bényi) The Sobolev inequality on the torus revisited, Publ. Math. Debrecen 83 (2013), no. 3, 359--374.
104. (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.
105. (with J. Quastel) On invariant Gibbs measures conditioned on mass and momentum, J. Math. Soc. Japan 65 (2013), no. 1, 13--35.
106. (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.
107. (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.
108. (with S. Kwon) On unconditional well-posedness of modified KdV, Int. Math. Res. Not. 2012, no. 15, 3509--3534.
109. (with C. Sulem) On the one-dimensional cubic nonlinear Schrödinger equation below L², Kyoto J. Math. 52 (2012), no.1, 99--115.
110. (with Á. Bényi) Modulation spaces, Wiener amalgam spaces, and Brownian motions, Adv. Math. 228 (2011), no. 5, 2943--2981.
111. Remarks on nonlinear smoothing under randomization for the periodic KdV and the cubic Szegö equation, Funkcial. Ekvac. 54 (2011), no. 3, 335--365.
112. 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.
113. (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.
114. (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.
115. Periodic stochastic Korteweg-de Vries equation with additive space-time white noise, Anal. PDE 2 (2009), no. 3, 281--304.
116. 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''.
117. Invariance of the Gibbs measure for the Schrödinger-Benjamin-Ono system, SIAM J. Math. Anal. 41 (2009/10), no. 6, 2207--2225.
118. Invariant Gibbs measures and a.s. global well-posedness for coupled KdV systems, Differential Integral Equations 22 (2009), no. 7--8, 637--668.
119. Diophantine conditions in global well-posedness of coupled KdV-type systems, Electron. J. Differential Equations 2009, no. 52, 48 pp.
120. Diophantine conditions in well-posedness theory of coupled KdV-type systems: local theory, Int. Math. Res. Not. 2009, no. 18, 3516--3556.
121. (with Á. Bényi) Best Constants for Certain Multilinear Integral Operators, J. Inequal. Appl. 2006, Art. ID 28582, 12 pp.

• Introduction to partial differential equations, (with Y. Tsutsumi) Translation of the book by Y. Tsutsumi from Japanese to English, 99% complete.

• Math with Yuzhao, Birmingham, UK, Jul. 2022. (file size 46.3MB due to some photos).
• Stochastic PDEs with multiplicative noises, Edinburgh, Jan. - Apr., 2022.
• Gibbs measures, singular stochastic wave equations, and canonical stochastic quantization, Peking University, Oct. - Nov. 2021. Talk 1, Talk 2, Talk 3
• Singular stochastic dispersive PDEs, Edinburgh, Feb. - May, 2021.
• Singular stochastic nonlinear wave equations, Bonn, Sep. 2019. Lecture videos available on Youtube: Lec 1, Lec 2, Lec 3, Lec 4
• Two-dimensional statistical hydrodynamics, (lecture note taken by Andreia Chapouto), Edinburgh, Feb. - Mar., 2019.
• Paracontrolled distributions and singular stochastic PDEs, (lecture note taken by Justin Forlano), Edinburgh, Jan. - Apr., 2018.
• Stochastic dispersive dynamics, Chapters 0, 1, 2, Chapter 3, Bonn, Sep. 2017.
• Introduction to stochastic dispersive dynamics, RIMS, Kyoto, May 2017. Updated in Sep. 2017 (The statement on p.6 (on the stochastic convolution) has been corrected).
• A note on the stochastic nonlinear wave equations with a multiplicative space-time white noise on the circle, Apr. 2016.
• Invariant and quasi-invariant measures for Hamiltonian PDEs, Waseda, Oct. 2015.
• Ornstein-Uhlenbeck process on abstract Wiener spaces, hypercontractivity, and logarithmic Sobolev inequality, Jan. 2015.
• Strauss exponent and small data global existence: Strichartz estimate for non-admissble pair, Feb. 2012.
• Periodic L⁴-Strichartz estimate for KdV, Feb. 2012.
• Note on a lower bound of the Weyl sum in Bourgain's paper (GAFA '93), Aug. 2011. Updated in Nov. 2014.
• Note on the normal form and the I-method by Bourgain (JAM '04), Jun. 2010. Updated in Sep. 2016.
• Hamiltonian systems and invariant measures, Kyoto, Oct. 2010.
• Introduction to the well-posedness theory of dispersive PDEs, Toronto, Feb. 2010.
• Basic H¹-subcritical scattering theory: defocusing cubic NLS on ℝ³, Oct. 2009.
• Cauchy problem of the cubic NLS on 𝕋, Sep. 2009.
• Invariant Gibbs measure, white noise, a.s. GWP and all that, Toronto, Nov. 2008.
• The multiplier problem for the ball (by C. Fefferman, '71), 2006(?).

• Usama Nadeem (Sep. 2024 - Dec. 2024)
• Damiano Greco (Sep. 2024 - Aug. 2026)
• Guopeng Li (Sep. 2023 - Oct. 2024): tenure-track assistant professor at Beijing Institute of Technology, China
• Andreia Chapouto (Jul. 2023 - Sep. 2024): CNRS, France (2024 - ) and tenure-track assistant professor at Monash University, Australia (2025 - )
• Justin Forlano (Jul. 2023 - Dec. 2024): lecturer at Monash University, Australia (2025 - )
• Gyu Eun Lee (Sep. 2021 - Sep. 2022)
• Guangqu Zheng (Jul. 2021 - Sep. 2022): lecturer (= tenured assistant professor) at the University of Liverpool, UK
• Khalil Chouk (Oct. 2020 - Apr. 2021)
• Tristan Robert (Sep. 2018 - Aug. 2019): maître de conférence (= tenured assistant professor) at l'Université de Lorraine, France
• Dimitrios Roxanas (Sep. 2017 - Dec. 2018)
• Yuzhao Wang (Jan. 2016 - Aug. 2017): associate professor at the University of Birmingham, UK

• Mamoru Okamoto (Hiroshima University, Japan): Jan. 2025
• Yufei Shao (Beijing Institute of Technology, China): Sep. 2025 - Nov. 2025
• Shao Liu (University of Bonn, Germany): Aug. 2025 - Oct. 2025
• Kotaro Tsugawa (Chuo University, Japan): May 2025 - Mar. 2026
• Philippe Sosoe (Cornell University, USA): Jan. 2025 - Feb. 2025
• Tengfei Zhao (University of Science and Technology Beijing, China): Sep. 2023 - Aug. 2024
• Kihoon Seong (KAIST, Korea): Mar. 2020 - Aug. 2020
• Mamoru Okamoto (Shinshu University, Japan; currently at Osaka University, Japan): Apr. 2019 - Sep. 2019
• Soonsik Kwon (KAIST, Korea): Sep. 2015 - Aug. 2016

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