In the 1970s, Elias M. Stein introduced the Fourier restriction problem, which has received a lot of attention since then. Now it turns out that the Fourier restriction theory has many deep connections with other research areas such as PDE, geometric measure theory, analytic number theory, combinatorics, etc. See, for instance, the notes by Tao for more details.

I am interested in the topic known as Sharp Fourier Restriction Theory. This theory investigates the norm of Fourier restriction operators and related extremal problems. Foschi and Oliveira e Silva's survey shows some recent results in this research area. See also this survey written by Negro, Oliveira e Silva and Thiele.

I am also interested in the long-time dynamic and singularity formation of NLS, as well as related topics in the waveguide manifold setting. For more details, see the series of works by Dodson, I-team, and Merle-Raphael, etc.

Last but not least, part of my previous works are related to the weighted estimates for singular integrals on Gaussian measure spaces. Some background and progress on Gaussian Harmonic Analysis can be seen in Urbina Romero's book.

Some key words of my research: Fourier restriction estimates, sharp Fourier restriction theory, extremals (maximizers & extremizers), sharp constants, bilinear restriction estimates, refined Strichartz estimates, profile decomposition, mass concentration, blow-up solution, waveguide, weighted estimates, Gaussian measure spaces.