Preprints:
(with N. Tzvetkov) Large torus limit of global dynamics of the two-dimensional dispersive Anderson model, submitted (2025). arXiv link
(with S. Liu and T. Oh) Hyperbolic O(N) linear sigma model and its mean-field limit, submitted (2025). arXiv link
(with E. Brun, G. Li, and Y. Zine) Global well-posedness of one-dimensional fractional cubic nonlinear Schrödinger equations in negative Sobolev spaces, submitted (2023). arXiv link
(with N. Tzvetkov and Y. Wang) Existence, uniqueness, and universality of global dynamics for the fractional hyperbolic Φ43-model, submitted (2023). arXiv link
(with A. Chapouto and G. Li) Global dynamics for the stochastic nonlinear beam equations on the four-dimensional torus, to appear in Proc. Roy. Soc. Edinburgh Sect. A. arXiv link
Publications:
Local well-posedness of the periodic nonlinear Schrödinger equation with a quadratic nonlinearity \overline{u}2 in negative Sobolev spaces, J. Dynam. Differential Equations 37 (2025), no. 1, 509-538. arXiv link
(with E. Brun and G. Li) Global well-posedness of the energy-critical stochastic nonlinear wave equations, J. Differential Equations 397 (2024), 316-348. arXiv link
(with A. Debussche, N. Tzvetkov, and N. Visciglia) Global well-posedness of the 2D nonlinear Schrödinger equation with multiplicative spatial white noise on the full space, Probab. Theory Related Fields 189 (2024), no. 3-4, 1161-1218. arXiv link
(with T. Oh) 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. arXiv link
Global well-posedness of the two-dimensional stochastic viscous nonlinear wave equations, Stoch. Partial Differ. Equ. Anal. Comput. 12 (2024), no. 2, 898-931. arXiv link
On the probabilistic well-posedness of the two-dimensional periodic nonlinear Schrödinger equation with the quadratic nonlinearity |u|2, J. Math. Pures Appl. 171 (2023), 75-101. arXiv link
(with T. Oh) On the two-dimensional singular stochastic viscous nonlinear wave equations, C. R. Math. Acad. Sci. Paris 360 (2022), 1227-1248. arXiv link
(with G. Chasapis and T. Tkocz) Rademacher-Gaussian tail comparison for complex coefficients and related problems, Proc. Amer. Math. Soc. 150 (2022), no. 3, 1339-1349. arXiv link
(with T. Tkocz) A note on the extremal non-central sections of the cross-polytope, Adv. in Appl. Math. 118 (2020), 102031, 17pp. arXiv link
In preparation:
Weak universality of global dynamics for the fractional hyperbolic Φ43-model.
(with H. Koch) The Korteweg-de Vries limit for the global dynamics of the Toda lattice.