I study the well-posedness and asymptotics of hyperbolic equations, as well as some fundamental mathematical problems in the theory of General Relativity (GR). I have been working on the Kerr black hole stability conjecture (which aims to show the Kerr spacetime is stable against small perturbations), the Price's law (which predicts the sharp decay rates of various linear fields in Kerr spacetimes), and the Strong Cosmic Censorship conjecture (which concerns the problem of determinism in GR). I am also interested in other aspects of hyperbolic equations and GR.

Publications

• Mode stability on the real axis, with Lars Andersson, Claudio Paganini, and Bernard Whiting.

arXiv: 1607.02759, Journal of Mathematical Physics 58, 072501, 19pp, (2017).

• Uniform energy bound and Morawetz estimate for extreme components of spin fields in the exterior of a slowly rotating Kerr black hole I: Maxwell field.

    arXiv: 1705.06621, Annales Henri Poincaré 21, 815-863, 49pp, (2020). 

• Uniform energy bound and Morawetz estimate for extreme components of spin fields in the exterior of a slowly rotating Kerr black hole II: linearized gravity.

arXiv: 1708.07385, Communications in Mathematical Physics 377, 2489-2551, 63pp, (2020).

• Stability for the linearized gravity on the Kerr spacetime, with Lars Andersson, Thomas Bäckdahl, and Pieter Blue.

arXiv:1903.03859, Annals of PDE 11 (11), 161pp, (2025).

• Almost Price’s law in Schwarzschild and decay estimates in Kerr for Maxwell field.

arXiv: 2005.12492, Journal of Differential Equations 339, 89pp, (2022).

• Sharp decay estimates for massless Dirac fields on a Schwarzschild background, with Lin Zhang.

arXiv: 2008.11429, Journal of Functional Analysis 282 (6), 109375, 112pp, (2022).

• Price’s law for spin fields on a Schwarzschild background, with Lin Zhang.

arXiv:2104.13809, Annals of PDE 8 (25), 100pp, (2022).

• Nonlinear radiation gauge for near Kerr spacetimes, with Lars Andersson, Thomas Bäckdahl, and Pieter Blue.

arXiv: 2108.03148, Communications in Mathematical Physics 396 (1), 45-99, 46pp, (2022).

• Sharp decay for Teukolsky equation in Kerr spacetimes, with Lin Zhang.

arXiv:2111.04489, Communications in Mathematical Physics 401, 333-434, 102pp, (2023).

• Precise late-time asymptotics of scalar field in the interior of a subextreme Kerr black hole and its application in Strong Cosmic Censorship conjecture, with Lin Zhang.

arXiv:2208.08702, Transactions of the AMS 376 (11), 7815-7856, 42pp, (2023).

• Generically sharp decay for quasilinear wave equations with null condition, with Shijie Dong, Yue Ma, and Xu Yuan.

arXiv:2212.12115, 40pp, (2022).

• Energy-Morawetz estimates for the wave equation in perturbations of Kerr, with Jeremie Szeftel.

arXiv:2410.02341, 142pp, (2024).