| Private Homepage | https://www.uni-muenster.de/IVV5WS/WebHop/user/gholzege/ |
| Selected Publications | • Collingbourne, Sam C.; Holzegel, Gustav Uniform Boundedness for Solutions to the Teukolsky Equation on Schwarzschild from Conservation Laws of Linearised Gravity. Communications in Mathematical Physics Vol. 405, 2024 online • Dafermos, Mihalis; Holzegel, Gustav; Rodnianski, Igor Boundedness and decay for the Teukolsky equation on Kerr spacetimes I: the case |a|≪M. Annals of PDE Vol. 5, 2019, pp Paper No. 2, 118 online • Dafermos, Mihalis; Holzegel, Gustav; Rodnianski, Igor The linear stability of the Schwarzschild solution to gravitational perturbations. Acta Mathematica Vol. 222 (1), 2019 online • Graf, Olivier; Holzegel, Gustav Mode stability results for the Teukolsky equations on Kerr-anti-de Sitter spacetimes. Classical and Quantum Gravity Vol. 40 (4), 2023 online • Holzegel, Gustav Conservation laws and flux bounds for gravitational perturbations of the Schwarzschild metric. Classical and Quantum Gravity Vol. 33 (20), 2016, pp 205004 online • Holzegel, Gustav The wave equation on the Schwarzschild spacetime with small non-decaying first-order terms. Journal of Hyperbolic Differential Equations Vol. 20 (4), 2023 online • Holzegel, Gustav; Luk, Jonathan; Smulevici, Jacques; Warnick, Claude Asymptotic properties of linear field equations in anti-de Sitter space. Communications in Mathematical Physics Vol. 374, 2020, pp 1125-1178 online • Holzegel, Gustav; Shao, Arick Unique continuation from infinity in asymptotically anti-de Sitter spacetimes. Communications in Mathematical Physics Vol. 347 (3), 2016 online • Holzegel, Gustav; Shao, Arick The bulk-boundary correspondence for the Einstein equations in asymptotically anti-de Sitter spacetimes. Archive for Rational Mechanics and Analysis Vol. 247 (3), 2023 online • Speck, Jared; Holzegel, Gustav; Luk, Jonathan; Wong, Willie Stable Shock Formation for Nearly Simple Outgoing Plane Symmetric Waves. Annals of PDE Vol. 2 (2), 2016 online |
| Topics in Mathematics Münster | T6: Singularities and PDEs T7: Field theory and randomness |
| Current Publications | • Dafermos M, Holzegel G, Rodnianski I A scattering theory construction of dynamical vacuum black holes. Journal of Differential Geometry Vol. 126 (2), 2024 online • Collingbourne, Sam C.; Holzegel, Gustav Uniform Boundedness for Solutions to the Teukolsky Equation on Schwarzschild from Conservation Laws of Linearised Gravity. Communications in Mathematical Physics Vol. 405, 2024 online • Graf, Olivier; Holzegel, Gustav Mode stability results for the Teukolsky equations on Kerr-anti-de Sitter spacetimes. Classical and Quantum Gravity Vol. 40 (4), 2023 online • Holzegel, G; Kauffman, C The wave equation on subextremal Kerr spacetimes with small non-decaying first order terms. , 2023 online • Holzegel, Gustav; Shao, Arick The bulk-boundary correspondence for the Einstein equations in asymptotically anti-de Sitter spacetimes. Archive for Rational Mechanics and Analysis Vol. 247 (3), 2023 online • Holzegel, Gustav The wave equation on the Schwarzschild spacetime with small non-decaying first-order terms. Journal of Hyperbolic Differential Equations Vol. 20 (4), 2023 online • Dafermos, M; Holzegel, G; Rodnianski, I; Taylor, M Quasilinear wave equations on asymptotically flat spacetimes with applications to Kerr black holes. , 2022 online • Dafermos, M; Holzegel, G; Rodnianski, I; Taylor, M The non-linear stability of the Schwarzschild family of black holes. , 2021 online • Holzegel, Gustav; Luk, Jonathan; Smulevici, Jacques; Warnick, Claude Asymptotic properties of linear field equations in anti-de Sitter space. Communications in Mathematical Physics Vol. 374, 2020, pp 1125-1178 online |
| Current Projects | • EXC 2044 - T06: Singularities and PDEs Our goal is to utilise and further develop the theory of non-linear PDEs to understand singular phenomena arising in geometry and in the description of the physical world. Particular emphasis is put on the interplay of geometry and partial differential equations and also on the connection with theoretical physics. The concrete research projects range from problems originating in geometric analysis such as understanding the type of singularities developing along a sequence of four-dimensional Einstein manifolds, to problems in evolutionary PDEs, such as the Einstein equations of general relativity or the Euler equations of fluid mechanics, where one would like to understand the formation and dynamics (in time) of singularities. online • EXC 2044 - T07: Field theory and randomness Quantum field theory (QFT) is the fundamental framework to describe matter at its smallest length scales. QFT has motivated groundbreaking developments in different mathematical fields: The theory of operator algebras goes back to the characterisation of observables in quantum mechanics; conformal field theory, based on the idea that physical observables are invariant under conformal transformations of space, has led to breakthrough developments in probability theory and representation theory; string theory aims to combine QFT with general relativity and has led to enormous progress in complex algebraic geometry, among others. online • CRC 1442 - B06: Einstein 4-manifolds with two commuting Killing vectors We will investigate the existence, rigidity and classification of 4-dimensional Lorentzian and Riemannian Einstein metrics with two commuting Killing vectors. Our goal is to address open questions in the study of black hole uniqueness and gravitational instantons. In the Ricci-flat case, the problem reduces to the analysis of axisymmetric harmonic maps from R^3 to the hyperbolic plane. In the case of negative Ricci curvature, a detailed understanding of the conformal boundary value problem for asymptotically hyperbolic Einstein metrics is required. | gholzege@uni-muenster.de |
| Phone | +49 251 83-33743 |
| Room | 519 |
| Secretary | Sekretariat Holzegel Frau Anke Pietsch Telefon +49 251 83-33901 Zimmer 306 Das Sekretariat ist montags bis donnerstags von 08:00 bis 13:00 geöffnet. |
| Address | Herr Prof. Dr. Gustav Holzegel Mathematisches Institut Fachbereich Mathematik und Informatik der Universität Münster Einsteinstrasse 62 48149 Münster Deutschland |
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