Research

My research is centered around Einstein equations of general relativity. These equations form a system of geometric nonlinear partial differential equations and exhibit a hyperbolic structure. The mathematical techniques I use are related to nonlinear hyperbolic and elliptic equations, Riemannian and Lorentzian geometry, and functional analysis. More specifically, my work is centered on the stability of Minkowski spacetime, the stability of Kerr spacetimes, the formation of Big Bang singularities, the formation of trapped surfaces, the construction of spacelike initial data.

I am also interested in Quantum Field Theory on curved spacetimes and I have worked on Feynman problems and Lorentzian index theorem. I am particularly interested in applications of methods from microlocal analysis and spectral theory.

Publications and Preprints

1. Stability of Big Bang Singularity for the Einstein-Maxwell-Scalar Field-Vlasov System in the Full Strong Sub-Critical Regime (with Xinliang An and Taoran He), arXiv:2507.18585 (56 p.), 2025

2. Formation of multiple Black Holes from Cauchy data (with Jingbo Wan), arXiv:2506.16117 (88 p.), 2025

3. Formation of trapped surfaces for the Einstein-Maxwell-charged scalar field system (with Jingbo Wan), arXiv:2504.19976 (99 p.), 2025

4. A canonical foliation on null infinity in perturbations of Kerr (with Sergiu Klainerman and Jingbo Wan), arXiv:2412.20119 (82 p.), 2024

5. Exterior stability of Minkowski spacetime with borderline decay, arXiv:2405.00735 (38 p.), 2024

6. Angular momentum memory effect (with Xinliang An and Taoran He), arXiv:2403.11133 (6 p.), 2024

7. Global stability of Minkowski spacetime with minimal decay, arXiv:2310.07483 (94 p.), 2023

8. Kerr stability in external regions, Annals of PDE, 10, Art. 9, 147 pp., 2024

9. Stability of Minkowski spacetime in exterior regions, Pure and Applied Mathematics Quarterly, 20 (2), 757–868, 2024

10. Construction of GCM hypersurfaces in perturbations of Kerr, Annals of PDE, 9 (1), Art. 11, 112 pp., 2023

11.  An index theorem on asymptotically static spacetimes with compact Cauchy surface (with Michał Wrochna), Pure and Applied Analysis, 4 (4), 727–766, 2022