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My research is supported by the NSF grant DMS-2306143 "Physical-Space Estimates on Black Hole Perturbations" and the NSF CAREER grant DMS-2336118 "Gravitational and Electromagnetic Waves on Black Holes". I was previously supported by NSF grant DMS-2128386 "The Mathematical Theory of Black Holes with Matter".

I am a Sloan Research Fellow and a Simons Junior Faculty Fellow, supported by the Sloan Foundation and the Simons Foundation.

I received the Frontiers of Science Award in General Relativity in 2023 and the AWM Dissertation Prize in 2020.

You can find my Google scholar account here. You can find my doctoral thesis here.


Publications

  1. Physical-space estimates for axisymmetric waves on extremal Kerr spacetime
    with Jingbo Wan,
    J. Functional Anal., Vol. 287, Issue 12, 110668 (2024), here is the arXiv version.

  2. The Carter tensor and the physical-space analysis in perturbations of Kerr-Newman spacetime
    J. Differential Geom., Vol. 127, No. 1, pp. 277-371 (2024), here is the arXiv version.

  3. Electromagnetic-gravitational perturbations of Kerr-Newman spacetime: the Teukolsky and Regge-Wheeler equations
    J. Hyperbolic Differ. Equ., Vol. 19, No. 01, pp. 1-139 (2022), here is the arXiv version.

  4. Numerical computation of second order vacuum perturbations of Kerr black holes
    with Justin L. Ripley, Nicholas Loutrel, and Frans Pretorius,
    Phys. Rev. D 103, 104018 (2021), here is the arXiv version.

  5. Second order perturbations of Kerr black holes: Formalism and reconstruction of the first order metric
    with Nicholas Loutrel, Justin L. Ripley and Frans Pretorius,
    Phys. Rev. D 103, 104017 (2021), here is the arXiv version.

  6. The linear stability of Reissner-Nordström spacetime: the full subextremal range
    Commun. Math. Phys. 380, 1313–1360 (2020), here is the arXiv version.

    7. This paper was awarded the Frontiers of Science Award in the subfield of General Relativity.

  7. The linear stability of Reissner-Nordström spacetime for small charge
    Ann. PDE 6, 8 (2020), here is the arXiv version.

  8. Boundedness and decay for the Teukolsky system of spin 1 on Reissner-Nordström spacetime: the l=1 spherical mode
    Class. Quantum Grav., 36, 205001 (2019), here is the arXiv version.

  9. Boundedness and decay for the Teukolsky system of spin 2 on Reissner-Nordström spacetime: the case of small charge
    Ann. Henri Poincaré, 21, 2485–2580 (2020) , here is the arXiv version.

  10. Coupled gravitational and electromagnetic perturbations of Reissner-Nordström spacetime in a polarized setting
    Adv. Theo. Math. Phys., 24, 4, 979-1025 (2020), here is the arXiv version.

  11. On the local extension of Killing vector fields in electrovacuum spacetimes
    Ann. Henri Poincaré, 20, 2271–2293 (2019), here is the arXiv version.

Research Monographs

  1. Wave equation estimates and the nonlinear stability of slowly rotating Kerr black holes
    with Sergiu Klainerman and Jérémie Szeftel,
    to appear in Pure and Applied Mathematics Quarterly, here is the arXiv version (2022).

    Here is a Quanta article about this paper.


Preprints

  1. Boundedness and Decay for the Teukolsky System in Kerr-Newman Spacetime II: The Case |a|≪M, |Q|< M in axial symmetry
    with Jingbo Wan, here is the arXiv version (2024).

  2. Boundedness and Decay for the Teukolsky System in Kerr-Newman Spacetime I: The Case |a|,|Q|≪M
    here is the arXiv version (2023).

  3. A general formalism for the stability of Kerr
    with Sergiu Klainerman and Jérémie Szeftel, here is the arXiv version (2020).


Expository Surveys

  1. Recent progress on the stability of charged black holes
    Proceedings of the International Congress of Basic Science (2024)

  2. The Mathematics of Stable Black Holes
    Notices of the AMS, Vol.70, Number 4, 552-563 (2023), (also translated in Chinese for Mathematical Advances in Translation), here is the pdf version

  3. Stable black holes: in vacuum and beyond
    Bulletin (New Series) of the American Mathematical Society, Vol.60, Number 1, 1-27 (2023)

  4. The stability of black holes with matter
    Current Events Bulletin Booklet, American Mathematical Society (2022)

  5. The stability of charged black holes
    Mathematisches Forschungsinstitut Oberwolfach, Report No. 40 (2021), 43–46