Fully nonlinear elliptic equations
Fully nonlinear elliptic equations
On singular sets of fully nonlinear uniformly elliptic equations, arXiv:2608.18217 [math.AP].
Nirenberg's theorem and singular solutions from traceless symmetric matrices, arXiv:2609.25416 [math.AP].
Singular solutions from simple Euclidean Jordan algebras, arXiv:2611.04378 [math.AP].
Applied math
The minimal width of neural networks and immersions of real projective space (joint with B. Weinkove), arXiv:2610.20229 [stat.ML].
Conformally invariant equations
Liouville theorems for conformally invariant fully nonlinear equations. I (joint with Y.Y. Li and Z. Li), arXiv:2311.07542 [math.AP].
On the fully nonlinear Yamabe problem with constant boundary mean curvature. I (joint with Y.Y. Li and Z. Li), arXiv:2410.09683 [math.AP].
Liouville theorem with boundary conditions from Chern--Gauss--Bonnet formula (joint with Y.Y. Li and Z. Li), arXiv:2410.16384 [math.AP]. Part of this preprint to appear in American Journal of Mathematics.
On the Fully Nonlinear Yamabe Problem, Ph.D. Dissertation, Rutgers, The State University of New Jersey, 2025.
Travels
TBD, Informal Geometric Analysis Seminar, Northwestern University, Evanston, USA, TBD.
Academic Visitor, Northwestern University, Evanston, USA, Jun 21-26, 2026.
Some recent progress on the fully nonlinear Yamabe problem, Geometry and Analysis Seminar, University of California - Santa Crutz, USA, Jan 21, 2026.
Some recent progress on the fully nonlinear Yamabe problem, Analysis Seminar, University of California - Irvine, USA, Jan 13, 2026.
Some recent developments on the fully nonlinear Yamabe problem (Online Talk), Geometry and Topology Seminar, McMaster University, Canada, Nov 20, 2025.
Some recent developments on the fully nonlinear Yamabe problem, Seminar in Differential Geometry, University of California - San Diego, USA, Nov 13, 2025.
Optimal Liouville theorems for second order conformally invariant equations, 45-minute talk, Special Session on "Nonlinear Elliptic PDEs and Geometry”, AMS Western Sectional Meeting on 2025 Fall, University of Denver, Denver, USA, Aug 23-24, 2025.
Optimal Liouville theorems for second order conformally invariant equations, Workshop on Topics in Differential Geometry, Brown University, Providence, USA, Jun 11-13, 2025.
Some recent developments on the fully nonlinear Yamabe problems, Analysis Seminar, Northwestern University, Evanston, USA, Apr 7, 2025.
Liouville theorems for conformally invariant fully nonlinear equations, Special session on "Regularity of Nonlinear Equations and Free Boundary Problems", AMS Eastern Sectional Meeting on Fall 2024, University at Albany--State University of New York, Albany, USA, Oct 19-20, 2024.
Maximum principle for singular solutions of nonlinear elliptic equations and its applications, A Mini Course on PDEs, Beijing Normal University, Beijing, China, June 24-26, 2024.
Academic Visitor, City University of Hong Kong, Hong Kong, May 7-17, 2024.
Optimal Liouville theorems for fully nonlinear conformally invariant equations, Special Session on "Dynamics and Regularity of PDEs", Joint Mathematics Meetings (JMM) 2024, San Francisco, USA, Jan 5, 2024.
Conformally invariant elliptic equations: Liouville and Yamabe, Geometric Analysis Seminar, Xiamen University, Xiamen, China, Jun 1, 2023.
On the Liouville theorems and viscosity solutions, A Mini Course on PDEs, Beijing Normal University, Beijing, China, May 10, 2023.
Services
Co-organizer (with Z. Li, B. Weinkove, and Z. Yang), AMS Special Session on "Recent Developments in Elliptic PDEs and Related Problems", Joint Mathematics Meetings (JMM) 2027, Chicago, I.L., Jan 12-15, 2027.
Co-organizer (with Z. Li), AMS Special Session on "Recent Advances in Elliptic PDEs and Their Applications", Joint Mathematics Meetings (JMM) 2026, Washington, D.C., Jan 6-7, 2026.