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.

- 1. Late-time tails and mode coupling of linear waves on Kerr spacetimes (2021), (with Y. Angelopoulos and S. Aretakis)
- 2. Price’s law and precise late-time asymptotics for subextremal Reissner–Nordström black holes (2021), (with Y. Angelopoulos and S. Aretakis)
- 3. Curvature blow-up rates in spherically symmetric gravitational collapse to a Schwarzschild black hole (2020), (with X. An)
- 4. Quasinormal modes in extremal Reissner–Nordström spacetimes (2019), (with C. Warnick), in Comm. Math. Phys. 385, 1395–1498 (2021).
- 5. A model problem for quasinormal ringdown on asymptotically flat or extremal black holes (2019), (with C. Warnick), in JMP 61, 102501 (2020)
- 6. 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).
- 7. Nonlinear scalar perturbations of extremal Reissner–Nordström spacetimes (2019), (with Y. Angelopoulos and S. Aretakis), Annals of PDE, 6:12 (2020)
- 8. 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).
- 9. 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.
- 11. 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 .
- 12. The interior of dynamical extremal black holes in spherical symmetry (2017) (with J. Luk), in Pure Appl. Anal., 1:2, 263–326, (2019) .
- 13. 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).
- 14. A vector field approach to almost-sharp decay for the wave equation on spherically symmetric, stationary spacetimes (2016), (with Y. Angelopoulos and S. Aretakis), Annals of PDE, 4:15 (2018) .
- 15. Asymptotic blow-up for a class of semilinear wave equations on extremal Reissner-Nordström spacetimes (2016) (with Y. Angelopoulos and S. Aretakis).
- 16. The trapping effect on degenerate horizons (2015) (with Y. Angelopoulos and S. Aretakis), in Ann. Henri Poincaré 18, 1593–1633 (2017).
- 17. Linear waves in the interior of extremal black holes II (2015), Ann. Henri Poincaré 18, 4005–4081 (2017).
- 18. Linear waves in the interior of extremal black holes I (2015), in Comm. Math. Phys. 353, 717–770 (2017).
- 19. Linear waves on constant radius limits of cosmological black hole spacetimes (2014), Adv. in Theor. and Math. Phys., 22:4, 919–1005 (2018).

- • New Trends in Geometric PDEs, University of Münster, November 2021
- • Oberseminar, MPI MiS Leipzig, 14 September 2021
- • Oberwolfach workshop “Mathematical Aspects of General Relativity”, August–September 2021
- • Mathematics Online Lunch Seminar, Radboud University, 3 June 2021
- • Quantum & Gravity Seminar, Radboud University, 9 April 2021
- • AMS Sectional meeting (online), 21 March 2021,
- • DAMTP Friday GR seminar, University of Cambridge, 12 February 2021
- • Analysis Webinar, Loughborough University, 25 November 2020
- • Analysis Seminar, Caltech, 29 October 2020
- • Seminar on Quantum Field Theory, Gravitation and Elementary Particles, Leipzig University, 22 June 2020
- • Analysis Seminar, University of Leeds, 27 May 2020
- • CMSA General Relativity Seminar, Harvard University, 15 May 2020
- • Mini-Workshop on Wave Equations, Queen Mary University London, 29 January 2020
- • International Conference on Geometric Analysis and Hyperbolic Equations, Guangxi Center for Mathematical Research, December 2019
- • Analysis Seminar, Princeton University, 18 November 2019
- • General Relativity, Geometry and Analysis: beyond the first 100 years after Einstein, Institut Mittag-Leffler, 5 November 2019
- • PDE CDT Lunchtime seminar, University of Oxford, 17 October 2019
- • Analysis and PDE Seminar, University of California, Berkeley, 29 April 2019
- • Analysis & PDE Seminar, National University of Singapore, 28 March 2019
- • Junior Analysis Seminar, Imperial College London, 16 November 2018
- • Conference on Mathematical General Relativity, IHP, Paris, 28 May– 1 June 2018
- • DAMTP Friday GR seminar, University of Cambridge, 23 February 2018
- • Analysis and PDE seminar, Stanford University, 4 December 2017
- • Analysis Seminar, University of Edinburgh, 20 November 2017
- • Seminar on Mathematical General Relativity, UPMC, Paris, 6 June 2017
- • Analysis Seminar, Kings College London, 18 May 2017
- • Analysis Seminar, Princeton University, 24 April 2017
- • Warwick EPSRC Symposium: Geometric PDEs, University of Warwick, 12–16 December 2016
- • Pure analysis and PDE seminar, Imperial College London, 21 October 2016
- • Mathematical physics seminar, University of Grenoble, 18 May 2016
- • PDE seminar, CAMGSD, University of Lisbon, 4 May 2016
- • PDE CDT Lunchtime Seminar, University of Oxford, 10 March 2016
- • DAMTP Friday GR seminar, University of Cambridge, 26 February 2016
- • Junior Warwick–Imperial–Cambridge Geometric Analysis seminar, Queen Mary University of London, 6 January 2016
- • Focus Program on 100 Years of General Relativity, Fields Institute, University of Toronto, 9 June 2015