My main research concerns the Einstein equations of general relativity, a nonlinear system of hyperbolic PDEs that plays the central role in Einstein’s theory of gravity. In particular, I study precise mathematical aspects of the evolution of perturbations of black holes solutions to the Einstein equations and the nature of singularities in black hole interiors.

21. Late-time asymptotics for geometric wave equations with inverse-square potentials (2022)

20. On the Relation Between Asymptotic Charges, the Failure of Peeling and Late-time Tails (2022), (with L. Kehrberger)

19. Late-time tails and mode coupling of linear waves on Kerr spacetimes (2021), (with Y. Angelopoulos and S. Aretakis)

18. Price’s law and precise late-time asymptotics for subextremal Reissner–Nordström black holes (2021), (with Y. Angelopoulos and S. Aretakis)

17. Curvature blow-up rates in spherically symmetric gravitational collapse to a Schwarzschild black hole (2020), (with X. An)

16. Quasinormal modes in extremal Reissner–Nordström spacetimes (2019), (with C. Warnick), in Comm. Math. Phys. 385, 1395–1498 (2021).

15. A model problem for quasinormal ringdown on asymptotically flat or extremal black holes (2019), (with C. Warnick), in JMP 61, 102501 (2020)

14. A non-degenerate scattering theory for the wave equation on extremal Reissner–Nordström (2019), (with Y. Angelopoulos and S. Aretakis), in Comm. Math. Phys. 380, 323–408 (2020).

13. Nonlinear scalar perturbations of extremal Reissner–Nordström spacetimes (2019), (with Y. Angelopoulos and S. Aretakis), in Annals of PDE, 6:12 (2020)

12. Horizon hair of extremal black holes and measurements at null infinity (2018) (with Y. Angelopoulos and S. Aretakis), in Phys. Rev. Lett. 121, 131102 (2018).

11. Late-time asymptotics for the wave equation on extremal Reissner–Nordström backgrounds (2018), (with Y. Angelopoulos and S. Aretakis), in Adv. in Math. 375, 107363 (2020).

10. Asymptotics for scalar perturbations from a neighborhood of the bifurcation sphere (2018), (with Y. Angelopoulos and S. Aretakis), in Classical and Quantum Gravity, Vol. 35 (2018), 155007.

9. Logarithmic corrections in the asymptotic expansion for the radiation field along null infinity (2017), (with Y. Angelopoulos and S. Aretakis), in Journal of Hyperbolic Differential Equations, Vol. 16 (2019), No. 01, 1–34 .

8. The interior of dynamical extremal black holes in spherical symmetry (2017) (with J. Luk), in Pure Appl. Anal., 1:2, 263–326, (2019) .

7. Late-time asymptotics for the wave equation on spherically symmetric, stationary spacetimes (2016) (with Y. Angelopoulos and S. Aretakis), in Adv. in Math. 323, 529–621 (2018).

6. A vector field approach to almost-sharp decay for the wave equation on spherically symmetric, stationary spacetimes (2016), (with Y. Angelopoulos and S. Aretakis), in Annals of PDE, 4:15 (2018) .

5. Asymptotic blow-up for a class of semilinear wave equations on extremal Reissner-Nordström spacetimes (2016) (with Y. Angelopoulos and S. Aretakis).

4. The trapping effect on degenerate horizons (2015) (with Y. Angelopoulos and S. Aretakis), in Ann. Henri Poincaré 18, 1593–1633 (2017).

3. Linear waves in the interior of extremal black holes II (2015), in Ann. Henri Poincaré 18, 4005–4081 (2017).

2. Linear waves in the interior of extremal black holes I (2015), in Comm. Math. Phys. 353, 717–770 (2017).

1. Linear waves on constant radius limits of cosmological black hole spacetimes (2014), in Adv. in Theor. and Math. Phys., 22:4, 919–1005 (2018).

Azimuthal instabilities of extremal Kerr black holes (2021) in Oberwolfach Rep. 40