I have been dedicated to theoretical and applied research on nonlinear elliptic equations, with particular interest in PDE problems arising in conformal geometry and optimal constants in inequalities, asymptotic behavior analysis and numerical solutions of PDEs in computer graphics and topology optimization, as well as the application of machine proofs, symbolic computation, and artificial intelligence in PDE theory and numerical computation. I’m a member of Chinese Mathematical Society (CMS), life member of China Society for Industrial and Applied Mathematics (CSIAM), member of China Computer Federation (CCF), member of Anhui Society for Industrial and Applied Mathematics (AHSIAM).

The invariant tensor technique I proposed has resolved several open problems and conjectures in the classification of solutions for PDEs, manifold rigidity, optimal constants in geometric inequalities, and the classification of extremal functions. I answered the problem posed by Jerison-Lee [J. Amer. Math. Soc., 1988] concerning the theoretical framework of identities for critical exponent equations on the Heisenberg group; generalized the results of Biduat-Véron and Véron [Invent. Math., 1991] to CR manifolds, resolving the rigidity conjecture for subcritical exponent equations on pseudo-Hermitian manifolds proposed by Wang [Math Z., 2022], thereby extending the first-order Folland-Stein inequality established by Frank-Lieb [Ann. Math., 2012] on the CR sphere to pseudo-Hermitian manifolds; established a second-order Beckner inequality with optimal constants on closed manifolds and classified its extremal functions, extending Beckner’s [Ann. Math., 1993] second-order inequality from the sphere to general manifolds—the first higher-order geometric inequality with optimal constants on general manifolds; and established rigidity results for the critical exponent of semilinear equations with gradient terms in dimensions 5 and below, verifying a conjecture posed by Biduat-Véron, Huidobro, and Véron [Duke Math. J., 2019] for a certain range of q, representing the first rigidity result for equations with gradient terms. Furthermore, I have introduced symbolic computation methods into the techniques of integration by parts and invariant tensors, achieving initial progress toward semi-automated computation of identities.