Photo credit: Allegra Boverman

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 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 Dirichlet-to-Neumann 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.
  
  International Mathematics Research Notices, May 11, 2021.


• 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 black-hole 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 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.


• Resonances for obstacles in hyperbolic space, joint with Maciej Zworski.
  
  Communications in Mathematical Physics, 359(2):699-731, 2018.


• Uniqueness of Kerr-Newman-de Sitter black holes with small angular momenta.
  
  Annales Henri Poincaré, 19(2):607-617, 2018.


• Non-linear stability of the Kerr-Newman-de Sitter family of charged black holes.
  
  Annals of PDE, 4(1):11, Apr 2018.


• 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.


• 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):801-837, 2017.


• Resonance expansions for tensor-valued waves on asymptotically Kerr-de Sitter spaces.
  
  Journal of Spectral Theory, 7:519-557, 2017.


• 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.


• 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.


• 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.


• Global analysis of quasilinear wave equations on asymptotically de Sitter spaces.
  
  Annales de l'Institut Fourier, 66(4):1285-1408, 2016.


• Non-trapping estimates at normally hyperbolic trapping, joint with András Vasy.
  
  Mathematical Research Letters, 21(6):1277-1304, 2014.


• 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

• 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.
  
  
• Non-linear 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.
  
  
• 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.
  
  
• Non-linear stability of Kerr-de 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

Download pdf.