Peter Hintz
Assistant Professor
Sloan Research Fellow
Department of Mathematics
MIT
Office: 2265
Email: phintz@mit.edu
CV
PDE/Analysis seminar
IAP 2021: Mathematics Lecture Series
Click here for the course website.
Teaching
In the spring semester 2021, I am teaching 18.157, Introduction to Microlocal Analysis. Click here for the course website.
In the spring semester 2020, I taught 18.950/9501, Differential Geometry. Click here for the course website.
In the summer of 2019, I taught an introductory course on scattering theory at the Summer Northwestern Analysis Program (SNAP 2019). Click here for the course website.
In the spring semester 2019, I taught 18.157, Introduction to Microlocal Analysis. Click here for the course website.
Papers and preprints

Quasinormal modes of small Schwarzschild–de Sitter black holes, joint with YuQing Xie.
Preprint, 2021.

Quasinormal modes and dual resonant states on de Sitter space, joint with YuQing Xie.
Preprint, 2021.

The DirichlettoNeumann map for a semilinear wave equation on Lorentzian manifolds, joint with Gunther Uhlmann and Jian Zhai.
Preprint, 2021.

Semiclassical propagation through cone points.
Preprint, 2021.

Resolvents and complex powers of semiclassical cone operators.
Preprint, 2020.

An inverse boundary value problem for a semilinear wave equation on Lorentzian manifolds, joint with Gunther Uhlmann and Jian Zhai.
Preprint, 2020.

A sharp version of Price's law for wave decay on asymptotically flat spacetimes.
Preprint, 2020.

Black hole gluing in de Sitter space.
Communications in Partial Differential Equations, 2021, online first. Get a free copy of the published version here (while available).

Linear stability of slowly rotating Kerr black holes, joint with Dietrich Häfner and András Vasy.
Inventiones mathematicae, 2020, online first.

Normally hyperbolic trapping on asymptotically stationary spacetimes.
Probability and Mathematical Physics, to appear.

Strong cosmic censorship in charged blackhole spacetimes: still subtle, joint with Vitor Cardoso, João Costa, Kyriakos Destounis, and Aron Jansen.
Phys. Rev. D 98(10), 104007, 2018.

Quasinormal Modes and Strong Cosmic Censorship, joint with Vitor Cardoso, João Costa, Kyriakos Destounis, and Aron Jansen,
Phys. Rev. Lett. 120(3), 031103, 2018. See also this Viewpoint: A possible Failure of Determinism in General Relativity by Harvey Reall. Popular science accounts are given by Berkeley News, New Scientist (paywall), Live Science.

Stability of Minkowski space and polyhomogeneity of the metric, joint with András Vasy.
Annals of PDE, 6:2 (2020).

Reconstruction of Lorentzian manifolds from boundary light observation sets, joint with Gunther Uhlmann.
International Mathematics Research Notices, rnx320, 2018.

Wave decay for starshaped obstacles in R^{3}: papers of Morawetz and Ralston revisited, joint with Maciej Zworski.
Mathematical Proceedings of the Royal Irish Academy, 117A(2):4762, 2017.

Resonances for obstacles in hyperbolic space, joint with Maciej Zworski.
Communications in Mathematical Physics, 359(2):699731, 2018.

Uniqueness of KerrNewmande Sitter black holes with small angular momenta.
Annales Henri Poincaré, 19(2):607617, 2018.

Nonlinear stability of the KerrNewmande Sitter family of charged black holes.
Annals of PDE, 4(1):11, Apr 2018.

The global nonlinear stability of the Kerrde Sitter family of black holes, joint with András Vasy.
Acta Mathematica, 220:1206, 2018. This work was featured in Quanta Magazine.

Analysis of linear waves near the Cauchy horizon of cosmological black holes, joint with András Vasy.
Journal of Mathematical Physics, 58(8):081509, 2017.

Boundedness and decay of scalar waves at the Cauchy horizon of the Kerr spacetime.
Commentarii Mathematici Helvetici, 92(4):801837, 2017.

Resonance expansions for tensorvalued waves on asymptotically Kerrde Sitter spaces.
Journal of Spectral Theory, 7:519557, 2017.

Asymptotics for the wave equation on differential forms on Kerrde Sitter space, joint with András Vasy.
Journal of Differential Geometry, 110(2):221279, 2018.

Quasilinear waves and trapping: Kerrde Sitter space, joint with András Vasy. Lecture notes on the `Global analysis...' paper listed above.
Journées équations aux dérivées partielles, 21(6):115, 2014.

Global analysis of quasilinear wave equations on asymptotically Kerrde Sitter spaces, joint with András Vasy.
International Mathematics Research Notices, 2016(17):53555426, 2016.

Global analysis of quasilinear wave equations on asymptotically de Sitter spaces.
Annales de l'Institut Fourier, 66(4):12851408, 2016.

Nontrapping estimates at normally hyperbolic trapping, joint with András Vasy.
Mathematical Research Letters, 21(6):12771304, 2014.

Semilinear wave equations on asymptotically de Sitter, Kerrde Sitter and Minkowski spacetimes, joint with András Vasy.
Analysis & PDE, 8(8):18071890, 2015.
Talks and presentations

Scattering theory and resonances.
Slides (with lots of movies) for a talk in the SPUR/RSI Lecture Series at MIT, July 2020.

Global stability problems in General Relativity.
Slides for a talk at a conference in Murramarang, Australia, March 2018.

Nonlinear stability via global analysis.
Slides for a talk at the Black Hole Initiative Colloquium, Harvard, February 2018.

Stability of Minkowski space and polyhomogeneity of the metric.
Slides for a talk at the conference Frontiers of Theory and Applications of Nonlinear PDE, Hong Kong, December 2017.

Reconstruction of Lorentzian manifolds from boundary light observation sets.
Slides for a talk at the University of California, Santa Cruz, May 2017.

Nonlinear stability of Kerrde Sitter spacetimes.
Video recording of a talk at the workshop 16w5066: Geometric and Spectral Methods in Partial Differential Equations, Oaxaca, December 2016.

Nonlinear stability of Kerrde Sitter black holes.
Slides for a talk at the University of Cambridge, October 2016.

Regularity of linear waves at the Cauchy horizon of black hole spacetimes.
Slides for a talk at the workshop Evolution Equations on Singular Spaces, Luminy, April 2016.
Ph.D. thesis
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