• I am interested in constructing solutions to semilinear partial differential equations including the Yamabe Equation, Allen-Cahn equation, (magnetic) Ginzburg-Landau Equation, and energy-critical heat equation. I am also interested in studying the stability and other properties of these solutions.

• I am interested in studying the best constant of some geometric inequalities such as Beckner's inequality, a higher order Moser-Trudinger inequality.

1. (With Y. Liu, J. Wei) Stable solutions of U(1)-Yang-Mills-Higgs Model in R4, preprint.

2. (With J. Wei, X. Zeng and Q. Zhang) Co-existence of Type II blow-ups with multiple blow-up rates for five-dimensional heat equation with critical nonlinear boundary conditions, preprint.

3. (With C. Gui, T. Li and J. Wei) On sharp Beckner’s inequality for axially symmetric functions on S6, preprint.

4. (With J. Andrade and J. Wei) Complete metrics with constant fractional higher order Q-curvature on the punctured sphere, The Journal of Geometric Analysis, 2023, 34(1), 6.

5. (With T. Li and J. Wei) On sharp Beckner’s inequality for axially symmetric functions on S4, to appear in Math Research Letters.

6. (With R.Lyu) 2D Thin obstacle problem with data at infinity, preprint.

1.  Stability of solutions to the U(1)-Yang-Mills-Higgs equation in R^4.

Jan 15, 2025, at National University of Singapore.

2. On sharp Beckner’s inequality for axially symmetric functions on S4, S6 and S8.

June 1, 2024, at Scholars Symposium on Nonlinear Analysis at Wuhan University of Technology.

3. On sharp Beckner’s inequality for axially symmetric functions on S4 and S6.

Nov 3, 2023, at Ming Li Colloquium at Wuhan University of Technology.