PROF. DR. GUSTAV HOLZEGEL
Mathematics Institute
Einsteinstrasse 62
48149 Münster
Office 519
Phone: +49 251 83 33743
Honors
- Alexander von Humboldt Professorship – Alexander von Humboldt Foundation
- ERC Consolidator Grant – European Research Council (ERC)
- ERC Starting Grant – European Research Council (ERC)
Teaching
- Lecture: Mathematik II für Studierende der Physik [104171]
- [Mon, – | | KP 404]
- [Thu, – | | KP 404]
- Advanced seminar: Topics in General Relativity [104173]
- [ – | Tue, – | ]
- Practice: Übungen zur Mathematik II für Studierende der Physik [104172]
- [Tue, – | ]
- [Wed, – | ]
- [Wed, – | ]
- [Tue, – | ]
- [Tue, – | ]
- [Tue, – | ]
- [Mon, – | ]
- [Wed, – | ]
- [Wed, – | ]
- [Mon, – | ]
- [Thu, – | ]
- [Thu, – | ]
- Colloquium: Kolloquium Partielle Differentialgleichungen [104370]
(in cooperation with Prof. Dr. Christian Seis and Prof. Dr. Hendrik Weber)- [ – | Tue, – | ]
- Lecture: Mathematik I für Studierende der Physik [102177]
- [ – | Mon, – | | KP 404]
- [ – | Thu, – | | KP 404]
- Advanced seminar: Topics in General Relativity [102174]
(in cooperation with Christopher Kauffman)- [ – | Tue, – | | M A 503 (SR 5)]
- Practice: Übungen zur Mathematik I für Studierende der Physik [102179]
- [ – | Mon, – | ]
- [ – | Tue, – | ]
- [ – | Tue, – | ]
- [ – | Mon, – | | M A 111 (SR 1C)]
- [ – | Mon, – | | M A 111 (SR 1C)]
- [ – | Tue, – | ]
- [ – | Tue, – | | M A 111 (SR 1C)]
- [ – | Tue, – | | M A 111 (SR 1C)]
- [ – | Tue, – | | M A 111 (SR 1C)]
- [ – | Wed, – | ]
- [ – | Wed, – | | M A 111 (SR 1C)]
- [ – | Wed, – | ]
- [ – | Thu, – | ]
- [ – | Thu, – | | M A 111 (SR 1C)]
- [Wed, – | | M A 111 (SR 1C)]
- [Wed, – | | M A 111 (SR 1C)]
- Colloquium: Kolloquium Partielle Differentialgleichungen [102369]
(in cooperation with Prof. Dr. Christian Seis and Prof. Dr. Hendrik Weber)- [ – | Tue, – | | SRZ 203]
- Advanced seminar: Topics in General Relativity [100173]
(in cooperation with Christopher Kauffman) - Colloquium: Kolloquium Partielle Differentialgleichungen [100342]
(in cooperation with Prof. Dr. Christian Seis and Prof. Dr. Hendrik Weber)
- Colloquium: Kolloquium Partielle Differentialgleichungen [108343]
(in cooperation with Prof. Dr. Christian Seis and Prof. Dr. Hendrik Weber)
- Seminar: Mathematical Methods of Classical Mechanics [106171]
(in cooperation with Prof. Dr. Hendrik Weber) - Seminar: Non-linear Wave equations [106170]
(in cooperation with Christopher Kauffman) - Advanced seminar: Topics in General Relativity [106169]
(in cooperation with Christopher Kauffman and Dr. Athanasios Chatzikaleas) - Colloquium: Kolloquium Partielle Differentialgleichungen [106168]
(in cooperation with Prof. Dr. Christian Seis and Prof. Dr. Hendrik Weber)
- Lecture: General Relativity and the Analysis of Black Hole Spacetimes [104588]
- Advanced seminar: Topics in General Relativity [104589]
(in cooperation with Christopher Kauffman and Dr. Athanasios Chatzikaleas) - Colloquium: Kolloquium Partielle Differentialgleichungen [104590]
(in cooperation with Prof. Dr. Christian Seis and Prof. Dr. Hendrik Weber)
- Advanced seminar: Topics in General Relativity [102114]
(in cooperation with Christopher Kauffman) - Advanced seminar: Oberseminar Partielle Differentialgleichungen [102113]
(in cooperation with Prof. Dr. Christian Seis and Prof. Dr. Hendrik Weber)
- Lecture: Non-Linear Wave equations [100140]
(in cooperation with Christopher Kauffman) - Advanced seminar: Oberseminar Partielle Differentialgleichungen [100143]
(in cooperation with Prof. Dr. Christian Seis and Prof. Dr. Hendrik Weber) - Advanced seminar: Topics in General Relativity [100142]
(in cooperation with Christopher Kauffman) - Practice: Übungen zu Non-Linear Wave equations [100141]
(in cooperation with Christopher Kauffman)
- Lecture: General Relativity and the Analysis of Black Hole Spacetimes [106701]
- Seminar: Topics in General Relativity [106700]
- Practice: Übungen zu General Relativity and the Analysis of Black Hole Spacetime [106549]
(in cooperation with Dr. Olivier Graf and Christopher Kauffman)
- Lecture: Non-linear Wave Equations [104260]
- Advanced seminar: Oberseminar zur Analysis [104369]
(in cooperation with Prof. Dr. Joachim Lohkamp, Prof. Dr. Angela Stevens, Dr. Sebastian Throm and Prof. Dr. André Schlichting) - Practice: Übungen zu Non-linear Wave Equations [104261]
- Lecture: Mathematik II für Studierende der Physik [104171]
Projects
In Process
- EXC 2044 - T06: Singularities and PDEs ()
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/2, T6 - EXC 2044 - T07: Field theory and randomness ()
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/2, T7 - CRC 1442 - B06: Einstein 4-manifolds with two commuting Killing vectors ()
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1442/2, B06
Finished
- EXC 2044 - B1: Smooth, singular and rigid spaces in geometry ()
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1 - EXC 2044 - C1: Evolution and asymptotics ()
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1 - EXC 2044 - C4: Geometry-based modelling, approximation, and reduction ()
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1 - The Black Hole Stability Problem and the Analysis of asymptotically anti-de Sitter spacetimes – BHSandAADS ()
EU-Project Hosted at University the of Münster: EC H2020 - ERC Consolidator Grant | Project Number: 772249 - Stability and Instability in the Mathematical Analysis of the Einstein equations – StabMAEinstein ()
Project Carried out outside the University Münster: EC FP 7 - ERC Starting Grant | Project Number: 337488
- EXC 2044 - T06: Singularities and PDEs ()
Publications
Selection
- Collingbourne, Sam C., and Holzegel, Gustav. . “Uniform Boundedness for Solutions to the Teukolsky Equation on Schwarzschild from Conservation Laws of Linearised Gravity.” Communications in Mathematical Physics 405 138. doi: 10.1007/s00220-024-04999-4.
- Holzegel, Gustav, and Shao, Arick. . “The bulk-boundary correspondence for the Einstein equations in asymptotically anti-de Sitter spacetimes.” Preprint. Archive for Rational Mechanics and Analysis 247 (3) 56. doi: 10.1007/s00205-023-01890-9.
- Graf, Olivier, and Holzegel, Gustav. . “Mode stability results for the Teukolsky equations on Kerr-anti-de Sitter spacetimes.” Classical and Quantum Gravity 40 (4) 045003. doi: 10.1088/1361-6382/acb0ac.
- Holzegel, Gustav. . “The wave equation on the Schwarzschild spacetime with small non-decaying first-order terms.” Journal of Hyperbolic Differential Equations 20 (4): 825–834. doi: 10.1142/S0219891623500273.
- Holzegel, Gustav, Luk, Jonathan, Smulevici, Jacques, and Warnick, Claude. . “Asymptotic properties of linear field equations in anti-de Sitter space.” Communications in Mathematical Physics 374: 1125–1178. doi: 10.1007/s00220-019-03601-6.
- Dafermos, Mihalis, Holzegel, Gustav, and Rodnianski, Igor. . “Boundedness and decay for the Teukolsky equation on Kerr spacetimes I: the case |a|≪M.” Annals of PDE 5: Paper No. 2, 118.. doi: 10.1007/s40818-018-0058-8.
- Dafermos, Mihalis, Holzegel, Gustav, and Rodnianski, Igor. . “The linear stability of the Schwarzschild solution to gravitational perturbations.” Acta Mathematica 222 (1): 1–214. doi: 10.4310/ACTA.2019.v222.n1.a1.
- Holzegel, Gustav. . “Conservation laws and flux bounds for gravitational perturbations of the Schwarzschild metric.” Classical and Quantum Gravity 33 (20): 205004.. doi: 10.1088/0264-9381/33/20/205004.
- Holzegel, Gustav, and Shao, Arick. . “Unique continuation from infinity in asymptotically anti-de Sitter spacetimes.” Communications in Mathematical Physics 347 (3): 723–775. doi: 10.1007/s00220-016-2576-0.
- Speck, Jared, Holzegel, Gustav, Luk, Jonathan, and Wong, Willie. . “Stable Shock Formation for Nearly Simple Outgoing Plane Symmetric Waves.” Annals of PDE 2 (2) 10. doi: 10.1007/S40818-016-0014-4.
Complete List
- Dafermos, M, Holzegel, G, and Rodnianski, I. . “A scattering theory construction of dynamical vacuum black holes.” Journal of Differential Geometry 126 (2): 633–740. doi: 10.4310/jdg/1712344221.
- Collingbourne, Sam C., and Holzegel, Gustav. . “Uniform Boundedness for Solutions to the Teukolsky Equation on Schwarzschild from Conservation Laws of Linearised Gravity.” Communications in Mathematical Physics 405 138. doi: 10.1007/s00220-024-04999-4.
- Holzegel, Gustav, and Shao, Arick. . “The bulk-boundary correspondence for the Einstein equations in asymptotically anti-de Sitter spacetimes.” Preprint. Archive for Rational Mechanics and Analysis 247 (3) 56. doi: 10.1007/s00205-023-01890-9.
- Graf, Olivier, and Holzegel, Gustav. . “Mode stability results for the Teukolsky equations on Kerr-anti-de Sitter spacetimes.” Classical and Quantum Gravity 40 (4) 045003. doi: 10.1088/1361-6382/acb0ac.
- Holzegel, G, and Kauffman, C. . “The wave equation on subextremal Kerr spacetimes with small non-decaying first order terms.” Preprint. arXiv doi: 10.48550/arXiv.2302.06387.
- Holzegel, Gustav. . “The wave equation on the Schwarzschild spacetime with small non-decaying first-order terms.” Journal of Hyperbolic Differential Equations 20 (4): 825–834. doi: 10.1142/S0219891623500273.
- Dafermos, M, Holzegel, G, Rodnianski, I, and Taylor, M. . “Quasilinear wave equations on asymptotically flat spacetimes with applications to Kerr black holes.” Preprint. arXiv doi: 10.48550/arXiv.2212.14093.
- Dafermos, M, Holzegel, G, Rodnianski, I, and Taylor, M. . “The non-linear stability of the Schwarzschild family of black holes.” Preprint. arXiv doi: 10.48550/arXiv.2104.08222.
- Holzegel, Gustav, Luk, Jonathan, Smulevici, Jacques, and Warnick, Claude. . “Asymptotic properties of linear field equations in anti-de Sitter space.” Communications in Mathematical Physics 374: 1125–1178. doi: 10.1007/s00220-019-03601-6.
- Holzegel, G, and Kauffman, C. . “A note on the wave equation on black hole spacetimes with small non-decaying first order terms.” Preprint. arXiv doi: 10.48550/arXiv.2005.13644.
- Dafermos, Mihalis, Holzegel, Gustav, and Rodnianski, Igor. . “Boundedness and decay for the Teukolsky equation on Kerr spacetimes I: the case |a|≪M.” Annals of PDE 5: Paper No. 2, 118.. doi: 10.1007/s40818-018-0058-8.
- Dafermos, Mihalis, Holzegel, Gustav, and Rodnianski, Igor. . “The linear stability of the Schwarzschild solution to gravitational perturbations.” Acta Mathematica 222 (1): 1–214. doi: 10.4310/ACTA.2019.v222.n1.a1.
- Holzegel, G, and Shao, A. . “Unique continuation from infinity in asymptotically anti-de Sitter spacetimes II: Non-static boundaries.” Communications in Partial Differential Equations 42 (12): 1871–1922. doi: 10.1080/03605302.2017.1390677.
- Holzegel, Gustav. . “Conservation laws and flux bounds for gravitational perturbations of the Schwarzschild metric.” Classical and Quantum Gravity 33 (20): 205004.. doi: 10.1088/0264-9381/33/20/205004.
- Holzegel, G, Klainerman, S, Speck, J, and Wong, W. . “Small-data shock formation in solutions to 3D quasilinear wave equations: An overview.” Journal of Hyperbolic Differential Equations 13 (1): 1–105. doi: 10.1142/S0219891616500016.
- Holzegel, Gustav, and Shao, Arick. . “Unique continuation from infinity in asymptotically anti-de Sitter spacetimes.” Communications in Mathematical Physics 347 (3): 723–775. doi: 10.1007/s00220-016-2576-0.
- Speck, Jared, Holzegel, Gustav, Luk, Jonathan, and Wong, Willie. . “Stable Shock Formation for Nearly Simple Outgoing Plane Symmetric Waves.” Annals of PDE 2 (2) 10. doi: 10.1007/S40818-016-0014-4.
- Holzegel, G, and Warnick, C. . “The Einstein–Klein–Gordon–AdS system for general boundary conditions.” Journal of Hyperbolic Differential Equations 12 (2): 293–342. doi: 10.1142/S0219891615500095.
- Holzegel, G, and Warnick, C. . “Boundedness and growth for the massive wave equation on asymptotically anti-de Sitter black holes.” Journal of Functional Analysis 226 (4): 2436–2485. doi: 10.1016/j.jfa.2013.10.019.
- Holzegel, G, and Smulevici, J. . “Quasimodes and a lower bound on the uniform energy decay rate for Kerr-AdS spacetimes.” Analysis and PDE 7 (5): 1057–1090. doi: 10.2140/apde.2014.7.1057.
- Holzegel, G, and Smulevici, J. . “Decay Properties of Klein-Gordon Fields on Kerr-AdS Spacetimes.” Communications on Pure and Applied Mathematics 66 (11): 1751–1802. doi: 10.1002/cpa.21470.
- Holzegel, G, and Smulevici, J. . “Stability of Schwarzschild-AdS for the sphericallysymmetric Einstein-Klein-Gordon system.” Communications in Mathematical Physics 317: 205–251. doi: 10.1007/s00220-012-1572-2.
- Holzegel, G. . “Well-posedness for the massive wave equation on asymptotically anti-de Sitter spacetimes.” Journal of Hyperbolic Differential Equations 9 (2): 239–261. doi: 10.1142/S0219891612500087.
- Holzegel, G, and Smulevici, J. . “Self-gravitating Klein–Gordon fields in asymptotically anti-de Sitter spacetimes.” Annales Henri Poincare 13: 991–1038. doi: 10.1007/s00023-011-0146-8.
- Holzegel, G. . “On the massive wave equation on slowly rotating Kerr-AdS spacetimes.” Communications in Mathematical Physics 294: 169–197. doi: 10.1007/s00220-009-0935-9.
- Holzegel, G. . “Stability and decay rates for the five-dimensional Schwarzschild metric under biaxial perturbations.” Advances in Theoretical and Mathematical Physics 14 (5): 1245–1372. doi: 10.4310/ATMP.2010.v14.n5.a1.
- Holzegel, G, Schmelzer, T, and Warnick, C. . “Ricci flows connecting Taub–Bolt and Taub–NUT metrics.” Classical and Quantum Gravity 24 (24): 6201–6217. doi: 10.1088/0264-9381/24/24/004.
- Dafermos, M, and Holzegel, G. . “On the nonlinear stability of higher dimensional triaxial Bianchi-{IX} black holes.” Advances in Theoretical and Mathematical Physics 10 (4): 503–523. doi: 10.4310/ATMP.2006.v10.n4.a2.
- Holzegel, G. . “On the instability of Lorentzian Taub–NUT space.” Classical and Quantum Gravity 23 (11): 3951–3962. doi: 10.1088/0264-9381/23/11/017.
- Gibbons, GW, and Holzegel, G. . “The positive mass and isoperimetric inequalities for axisymmetric black holes in four and five dimensions.” Classical and Quantum Gravity 23 (22): 6459–6478. doi: 10.1088/0264-9381/23/22/022.