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
- Kolloquium: Colloquium Partial Differential Equations [108343]
(in cooperation with Prof. Dr. Christian Seis, Prof. Dr. Hendrik Weber)
[ - | | wöchentlich | Di | SRZ 203 | Prof. Dr. Christian Seis]
- 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) - Oberseminar: Topics in General Relativity [106169]
(in cooperation with Christopher Kauffman, Dr. Athanasios Chatzikaleas) - Kolloquium: Colloquium Partial Differential Equations [106168]
(in cooperation with Prof. Dr. Christian Seis, Prof. Dr. Hendrik Weber)
- Vorlesung: General Relativity and the Analysis of Black Hole Spacetimes [104588]
- Oberseminar: Topics in General Relativity [104589]
(in cooperation with Christopher Kauffman, Dr. Athanasios Chatzikaleas) - Kolloquium: Colloquium Partial Differential Equations [104590]
(in cooperation with Prof. Dr. Christian Seis, Prof. Dr. Hendrik Weber)
- Oberseminar: Research Seminar on Partial Differential Equations [102113]
(in cooperation with Prof. Dr. Christian Seis, Prof. Dr. Hendrik Weber) - Oberseminar: Topics in General Relativity [102114]
(in cooperation with Christopher Kauffman)
- Vorlesung: Non-Linear Wave equations [100140]
(in cooperation with Christopher Kauffman) - Oberseminar: Research Seminar on Partial Differential Equations [100143]
(in cooperation with Prof. Dr. Christian Seis, Prof. Dr. Hendrik Weber) - Oberseminar: Topics in General Relativity [100142]
(in cooperation with Christopher Kauffman) - Tutorial Non-Linear Wave equations [100141]
(in cooperation with Christopher Kauffman)
- Vorlesung: General Relativity and the Analysis of Black Hole Spacetimes [106701]
- Seminar: Topics in General Relativity [106700]
- Tutorial: General Relativity and the Analysis of Black Hole Spacetime [106549]
(in cooperation with Dr. Olivier Graf, Christopher Kauffman)
- Vorlesung: Non-linear wave equations [104260]
- Oberseminar: Research Seminar on Analysis [104369]
(in cooperation with Prof. Dr. Joachim Lohkamp, Prof. Dr. Angela Stevens, Dr. Sebastian Throm, Prof. Dr. André Schlichting) - Tutorial: Non-linear wave equations [104261]
- Kolloquium: Colloquium Partial Differential Equations [108343]
Projects
In Process
- 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 - 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
Finished
- BHSandAADS – The Black Hole Stability Problem and the Analysis of asymptotically anti-de Sitter spacetimes ( – )
EU-Project Hosted at University the of Münster: EC H2020 - ERC Consolidator Grant | Project Number: 772249
- CRC 1442 - B06: Einstein 4-manifolds with two commuting Killing vectors ( – )
Publications
- . . ‘Mode stability results for the Teukolsky equations on Kerr-anti-de Sitter spacetimes.’ Classical and Quantum Gravity 40, № 4. doi: 10.1088/1361-6382/acb0ac.
- . The wave equation on subextremal Kerr spacetimes with small non-decaying first order terms arXiv. 0th Ed. . doi: 10.48550/arXiv.2302.06387.
- . . ‘The bulk-boundary correspondence for the Einstein equations in asymptotically anti-de Sitter spacetimes.’ Archive for Rational Mechanics and Analysis 247: 56. doi: 10.1007/s00205-023-01890-9.
- . Quasilinear wave equations on asymptotically flat spacetimes with applications to Kerr black holes arXiv. 0th Ed. . doi: 10.48550/arXiv.2212.14093.
- . The non-linear stability of the Schwarzschild family of black holes arXiv. 0th Ed. . doi: 10.48550/arXiv.2104.08222.
- . . ‘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.
- . A note on the wave equation on black hole spacetimes with small non-decaying first order terms arXiv. 0th Ed. . doi: 10.48550/arXiv.2005.13644.
- . . ‘Boundedness and decay for the Teukolsky equation on Kerr spacetimes I: the case |a|≪M.’ Annals of PDE 5, № 2: 1–118. doi: 10.1007/s40818-018-0058-8.
- . . ‘The linear stability of the Schwarzschild solution to gravitational perturbations.’ Acta Mathematica 222, № 1: 1–214. doi: 10.4310/ACTA.2019.v222.n1.a1.
- . . ‘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.
- . . ‘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.
- . . ‘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.
- . . ‘Unique continuation from infinity in asymptotically anti-de Sitter spacetimes.’ Communications in Mathematical Physics 347: 723–775. doi: 10.1007/s00220-016-2576-0.
- . . ‘The Einstein–Klein–Gordon–AdS system for general boundary conditions.’ Journal of Hyperbolic Differential Equations 12, № 2: 293–342. doi: 10.1142/S0219891615500095.
- . . ‘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.
- . . ‘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.
- . . ‘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.
- . . ‘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.
- . . ‘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.
- . . ‘Self-gravitating Klein–Gordon fields in asymptotically anti-de Sitter spacetimes.’ Annales Henri Poincare 13: 991–1038. doi: 10.1007/s00023-011-0146-8.
- . . ‘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.
- . . ‘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.
- . . ‘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.
- . . ‘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.
- . . ‘On the instability of Lorentzian Taub–NUT space.’ Classical and Quantum Gravity 23, № 11: 3951–3962. doi: 10.1088/0264-9381/23/11/017.
- . . ‘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.