Research

My research is centered around Einstein vacuum 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 precisely, my works focus on the stability of particular solutions of Einstein vacuum equations: the Minkowski spacetime and Kerr black holes.

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

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

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

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

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

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

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