My research lies in the intersection of analysis and probability, centered around (stochastic) PDEs and their invariant measures. My works are focused on the study of infinite dimensional Gibbs measures and their transport properties under the flow of hyperbolic/parabolic PDEs, such as invariance, quasi-invariance, and ergodicity. Another my focus is on well-posedness of singular SPDEs. The methods employed in this study exhibit a diverse range, spanning from analytic approaches to purely probabilistic methods, incorporating key concepts from PDE theory, stochastic analysis, and harmonic analysis.
- Phase transition of singular Gibbs measures for three-dimensional Schrödinger-wave system, arXiv:2306.17013
- Focusing Gibbs measures with harmonic potential (with T. Robert, L. Tolomeo, Y. Wang), arXiv:2212.11386
- Transport of Gaussian measures under the flow of one-dimensional fractional nonlinear Schrödinger equations (with J. Forlano), Comm. Partial Differential Equations, 47 (2022), no. 6, 1296-1337.
- Invariant Gibbs dynamics for the two-dimensional Zakharov-Yukawa system, arXiv:2111.11195
- A remark on Gibbs measures with log-correlated Gaussian fields (with T. Oh, L. Tolomeo), arXiv:2012.06729
- Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation in negative Sobolev spaces (with T. Oh), J. Funct. Anal. 281 (2021), no. 9, 109150, 49 pp.