My main research concerns the Einstein equations, a nonlinear system of hyperbolic PDEs that plays the central role in the theory of general relativity. In particular, I study precise mathematical aspects of the dynamical stability of black holes and the nature of singularities inside black hole solutions of the Einstein equations.

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

- • A vector field approach to almost-sharp decay for the wave equation on spherically symmetric, stationary spacetimes (2016) (with Y. Angelopoulos and S. Aretakis).

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

- • The trapping effect on degenerate horizons (2015) (with Y. Angelopoulos and S. Aretakis), in Ann. Henri Poincaré, Vol. 18 (2017), Issue 5, 1593–1633.

- • Linear waves in the interior of extremal black holes II (2015), Ann. Henri Poincaré, Vol. 18 (2017), Issue 12, 4005–4081.

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

- • Linear waves on constant radius limits of cosmological black hole spacetimes (2014), to appear in Adv. Theor. Math. Phys.

- • 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