Peter Hintz
Assistant Professor
Sloan Research Fellow
Department of Mathematics
MIT
Office: 2-265
E-mail: phintz@mit.edu
CV
PDE/Analysis seminar
IAP 2021: Mathematics Lecture Series
Click here for the course website.
Teaching
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
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Semiclassical propagation through cone points.
Preprint, 2021.
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Resolvents and complex powers of semiclassical cone operators.
Preprint, 2020.
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An inverse boundary value problem for a semilinear wave equation on Lorentzian manifolds, joint with Gunther Uhlmann and Jian Zhai.
Preprint, 2020.
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A sharp version of Price's law for wave decay on asymptotically flat spacetimes.
Preprint, 2020.
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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).
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Linear stability of slowly rotating Kerr black holes, joint with Dietrich Häfner and András Vasy.
Inventiones mathematicae, 2020, online first.
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Normally hyperbolic trapping on asymptotically stationary spacetimes.
Probability and Mathematical Physics, to appear.
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Strong cosmic censorship in charged black-hole spacetimes: still subtle, joint with Vitor Cardoso, João Costa, Kyriakos Destounis, and Aron Jansen.
Phys. Rev. D 98(10), 104007, 2018.
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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.
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Stability of Minkowski space and polyhomogeneity of the metric, joint with András Vasy.
Annals of PDE, 6:2 (2020).
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Reconstruction of Lorentzian manifolds from boundary light observation sets, joint with Gunther Uhlmann.
International Mathematics Research Notices, rnx320, 2018.
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Wave decay for star-shaped obstacles in R3: papers of Morawetz and Ralston revisited, joint with Maciej Zworski.
Mathematical Proceedings of the Royal Irish Academy, 117A(2):47-62, 2017.
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Resonances for obstacles in hyperbolic space, joint with Maciej Zworski.
Communications in Mathematical Physics, 359(2):699-731, 2018.
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Uniqueness of Kerr-Newman-de Sitter black holes with small angular momenta.
Annales Henri Poincaré, 19(2):607-617, 2018.
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Non-linear stability of the Kerr-Newman-de Sitter family of charged black holes.
Annals of PDE, 4(1):11, Apr 2018.
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The global non-linear stability of the Kerr-de Sitter family of black holes, joint with András Vasy.
Acta Mathematica, 220:1-206, 2018. This work was featured in Quanta Magazine.
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Analysis of linear waves near the Cauchy horizon of cosmological black holes, joint with András Vasy.
Journal of Mathematical Physics, 58(8):081509, 2017.
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Boundedness and decay of scalar waves at the Cauchy horizon of the Kerr spacetime.
Commentarii Mathematici Helvetici, 92(4):801-837, 2017.
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Resonance expansions for tensor-valued waves on asymptotically Kerr-de Sitter spaces.
Journal of Spectral Theory, 7:519-557, 2017.
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Asymptotics for the wave equation on differential forms on Kerr-de Sitter space, joint with András Vasy.
Journal of Differential Geometry, 110(2):221-279, 2018.
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Quasilinear waves and trapping: Kerr-de Sitter space, joint with András Vasy. Lecture notes on the `Global analysis...' paper listed above.
Journées équations aux dérivées partielles, 21(6):1-15, 2014.
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Global analysis of quasilinear wave equations on asymptotically Kerr-de Sitter spaces, joint with András Vasy.
International Mathematics Research Notices, 2016(17):5355-5426, 2016.
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Global analysis of quasilinear wave equations on asymptotically de Sitter spaces.
Annales de l'Institut Fourier, 66(4):1285-1408, 2016.
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Non-trapping estimates at normally hyperbolic trapping, joint with András Vasy.
Mathematical Research Letters, 21(6):1277-1304, 2014.
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Semilinear wave equations on asymptotically de Sitter, Kerr-de Sitter and Minkowski spacetimes, joint with András Vasy.
Analysis & PDE, 8(8):1807-1890, 2015.
Talks and presentations
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Scattering theory and resonances.
Slides (with lots of movies) for a talk in the SPUR/RSI Lecture Series at MIT, July 2020.
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Global stability problems in General Relativity.
Slides for a talk at a conference in Murramarang, Australia, March 2018.
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Non-linear stability via global analysis.
Slides for a talk at the Black Hole Initiative Colloquium, Harvard, February 2018.
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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.
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Reconstruction of Lorentzian manifolds from boundary light observation sets.
Slides for a talk at the University of California, Santa Cruz, May 2017.
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Non-linear stability of Kerr-de Sitter spacetimes.
Video recording of a talk at the workshop 16w5066: Geometric and Spectral Methods in Partial Differential Equations, Oaxaca, December 2016.
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Non-linear stability of Kerr-de Sitter black holes.
Slides for a talk at the University of Cambridge, October 2016.
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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
Download pdf.