My research interests are harmonic analysis (Euclidean/metric measure spaces/spaces of homogeneous type) and stochastic partial differential equations (SPDEs).
(Real) Local Hardy spaces, mean oscillations spaces (e.g. BMO, VMO, LMO and their non-homogeneous version), and their generalizations (such as Campanato spaces/Orlicz spaces/Besov, etc.)
Boundedness and compactness of Calderón-Zygmund singular integral operators, inhomogeneous Calderón-Zygmund singular integral operators, and their strongly singular version, on spaces mentioned above
Boundedness and compactness of commutators of the operators above with some functions $b$ (in BMO/CMO/LMO, etc.) from some space to another space
Fourier restriction conjecture (studied partly in my Master's degree) and related problems
PDE with periodic force
Existence and Uniqueness of solutions driven by (degenerate) Lévy process (with or without regime-switching) under variational approach (and semigroup approach)
Periodic measures via strong Feller property and irreducibility (as well as their weaker version - asymptotic strong Feller property and weakly irreducibility)
I am also interested in some other fields related to the above:
SPDEs driven by different processes, such as fractional Brownian motions or interesting processes;
quasi-linear/fully nonlinear SPDEs (certain interesting models there);
singular SPDEs (ergodicity, time-dependent coefficients) via different methods (e.g. rough paths integrals, paracontrolled distributions);
polynomial methods;
product setting and multi-parameter Hardy spaces and BMO-type spaces (and more);
connection of PDE theory and probability theory (such as potential theory and their probability counterpart)