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DPMMS

Centre for Mathematical Sciences

Wilberforce Road

Cambridge CB3 0WB

UK

CV

Nonlinear partial differential equations, general relativity, mathematical physics

Part II Linear analysisI will follow quite closely the lecture notes of Mihalis Dafermos. (Supplementary notes on Theorem 8.2)

Example Sheet 1 Example Sheet 2 Example Sheet 3 Example Sheet 4

Part III Introduction to nonlinear wave equationsLecture notes Review on Fourier analysis Example Sheet 1 Example Sheet 2 Example Sheet 3

- (with S.-J. Oh and S. Yang) Solutions to the Einstein-scalar-field system in spherical symmetry with large bounded variation norms, preprint.
- (with J. Speck, G. Holzegel and W. W.-Y. Wong) Stable shock formation for nearly plane symmetric waves, to appear in
Annals of PDE.- (with J. Sbierski) Instability results for the wave equation in the interior of Kerr black holes, to appear in
J. Funct. Anal.- (with G. Holzegel, J. Smulevici and C. Warnick) Asymptotic properties of linear field equations in anti-de Sitter space, preprint.
- (with S.-J. Oh) Proof of linear instability of the Reissner-Nordström Cauchy horizon under scalar perturbations, to appear in
Duke Math. J.- (with X. An) Trapped surfaces in vacuum arising from mild incoming radiation, to appear in
Adv. Theo. Math. Phys..- (with R. M. Strain) Strichartz estimates and moment bounds for the relativistic Vlasov-Maxwell system,
Arch. Rat. Mech. Anal.219(1):445-552, 2016 (combined from two earlier preprints in the 2D and 2.5D cases and the 3D case).- (with R. M. Strain ) A new continuation criterion for the relativistic Vlasov-Maxwell system,
Comm. Math. Phys., 331:1005-1027, 2014.- (with S.-J. Oh) Quantitative decay rates for dispersive solutions to the Einstein-scalar field system in spherical symmetry,
Analysis and PDE8(7):1603-1674, 2015.- Weak null singularities in general relativity, preprint.
- (with S. Klainerman and I. Rodnianski) A fully anisotropic mechanism for formation of trapped surfaces in vacuum,
Invent. Math.194(1):1–26, 2014.- (with I. Rodnianski) Nonlinear interaction of impulsive gravitational waves for the vacuum Einstein equations, preprint.
- (with I. Rodnianski) Local propagation of impulsive gravitational waves,
Comm. Pure and Appl. Math., 68(4):511–624, 2015.- On the local existence for the characteristic initial value problem in general relativity,
Int. Mat. Res. Notices, 20:4625-4678, 2012.- The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes,
Journal Eur. Math. Soc., 15(5):1629-1700, 2013.- A vector field method approach to improved decay for solutions to the wave equation on a slowly rotating Kerr black hole,
Analysis and PDE, 5(3):553-625, 2012.- Improved decay for solutions to the linear wave equation on a Schwarzschild black hole,
Annales Henri Poincare, 11:805-880, 2010.

Weak null singularities in general relativity, MSRI, November 2013. Formation of trapped surfaces, IHP, May 2013.