### Research Interests

Analysis, Partial Differential Equations, General Relativity

### Publications and Preprints

- (with R. Unger) Gravitational collapse to extremal black holes and the third law of black hole thermodynamics (2022), submitted

arXiv:2211.15742 - (with A. Figalli) On the prescribed negative Gauss curvature problem for graphs

Discrete Contin. Dyn. Syst. (2022)

arXiv:2209.02326 - (with J. P. G. Ramos) Uniqueness of solutions to nonlinear Schrödinger equations from their zeros

Annals of PDE 8, 21 (2022)

arXiv:2201.05109 - Blowup of the local energy of linear waves at the Reissner–Nordström–AdS Cauchy horizon

Class. Quantum Grav. 38 (2021) 214001

arXiv:2108.04280 - (with M. Van de Moortel) Strong Cosmic Censorship in the presence of matter: the decisive effect of horizon oscillations on the black hole interior geometry

Analysis & PDE (2022, to appear)

arXiv:2105.04604 - Diophantine approximation as Cosmic Censor for Kerr–AdS black holes

Invent. Math. 227 (2022), no. 3, 1169–1321

arXiv:2007.12614 - Uniform boundedness and continuity at the Cauchy horizon for linear waves on Reissner–Nordström–AdS black holes

Comm. Math. Phys. 376 (2020), no. 1, 145–200

arXiv:1812.06142 - (with Y. Shlapentokh-Rothman) A scattering theory for linear waves on the interior of Reissner–Nordström black holes

Ann. Henri Poincaré 20 (2019), no. 5, 1583–1650

arXiv:1804.05438 - The maximal excess charge for a family of density-matrix-functional theories including Hartree–Fock and Müller theories

J. Math. Phys. 58 (2017), no. 1, 011901

arXiv:1609.06272

### Oberwolfach reports

- On Strong Cosmic Censorship for Λ < 0

Oberwolfach Rep. 18 (2021), no. 3, pp. 2157–2267 - Scattering of linear waves on the interior of Reissner–Nordström black holes

Oberwolfach Rep. 15 (2018), pp. 2157–2251

### PhD Thesis

- Diophantine Approximation as Cosmic Censor for AdS Black Holes

Doctoral thesis, DPMMS, University of Cambridge (2020)