本科生课程：《数学分析》《数学物理方程》《泛函分析》《点集拓扑学》《实变函数与泛函分析》《微分几何》《复变函数》。

研究生课程：《实分析》《泛函分析》《现代偏微分方程入门》《二阶椭圆方程正则性理论》《变分法》等。

主持的科研项目
（1）两类几何偏微分方程能量等式及相关问题（编号：12671243），国家自然科学基金面上项目，2027.01～2030.12。
（2） 1/2-调和映照奇点集分层理论（编号：2024AFA061），湖北省自然科学基金杰出青年项目，2024.03～2027.03。
（3）Riviere型方程组正则性理论及其几何应用（编号：12271296），国家自然科学基金面上项目，2023.01～2026.12。
（4） Kirchhoff方程奇异摄动问题的研究（编号：11701045），国家自然科学基金青年项目，2018.01～2020.12。 
          

（1）Quantitative stratification and optimal regularity for harmonic almost complex structures. Adv. Math. 503 (2026), 111188.  (with C.-Y. Guo and Ming-Lun Liu)
（2）Quantitative regularity for minimizing intrinsic fractional harmonic maps. J. Differential Equations 463 (2026). https://doi.org/10.1016/j.jde.2026.114243. (With Yu-Ying Wang and Gao-Feng Zheng)
（3）A global regularity theory for sphere-valued fractional harmonic maps. Math. Z. 311 (2025), no. 4, Paper No. 89, 17 pp. (With Yu He and Gao-Feng Zheng)
（4）Optimal Higher Regularity for Biharmonic Maps Via Quantitative Stratification. Peking Math J. (2025) http://doi.org/10.1007/s42543-025-00107-0.  (with C.-Y. Guo, Gui-Chun Jiang and G.-F. Zheng)
（5）Lp-regularity of a geometrically nonlinear system in supercritical dimensions. Sci. China Math., 68 (2025), no. 10, 2313-2332. (With Chang-Yu Guo and Ming-Lun Liu) 
（6）Conservation law of harmonic mappings in supercritical dimensions. C. R. Math. Acad. Sci. Paris, 362 (2024), 769-773. (with Chang-Yu Guo)
（7）Lp-regularity for fourth order elliptic systems with antisymmetric potentials in higher dimensions. Calc. Var. Partial Differential Equations, 62:31, 2023. (with Chang-Yu Guo and Changyou Wang)
（8）Lp-regularity theory for even order elliptic systems with antisymmetric first order potentials. J. Math. Pures Appl. 165 (2022), 286-324. (with Chang-Yu Guo and Gao-Feng Zheng)
（9）The Lamm-Rivière system I: Lp-regularity theory. Calc. Var. Partial Differential Equations 60 (2021), no. 6, Paper No. 213, 32 pp. (with Chang-Yu Guo and Gao-Feng Zheng)
（10）Regularity of weak solutions to higher order elliptic systems in critical dimensions. Trans. Amer. Math. Soc. 374(5) (2021), 3579-3602. (with Chang-Yu Guo)
（11）Regularity of solutions for a fourth-order elliptic system via conservation law. J. London Math. Soc. 101(2) (2020), 907-922. (with Chang-Yu Guo)
（12）A singularly perturbed Kirchhoff problem revisited. J. Differential Equations 268 (2020), no. 2, 541-589. (with Gongbao Li, Peng Luo, Shuangjie Peng, Chunhua Wang) 
（13）Nonlinear Liouville problems in a quarter plane. Int. Math. Res. Not. IMRN 2017, 2207-2218. 
（14）Uniqueness and nondegeneracy of ground states for Choquard equations in three dimensions. Calc. Val. Partial Differential Equations 55 (2016), 55:134. 
（15）Asymptotic behaviors of solutions to quasilinear elliptic equations with critical Sobolev growth and Hardy potential. J. Differential Equations 259 (2015), 3929-3954.

教材：《测度论与函数空间讲义》（与别群益教授合作主编，科学出版社，2026）