Homepages
(this way to the possibly more complete Homepage in the old layout)
Klaus Kroencke
Fachbereich Mathematik Bereich AD Bundesstraße 55 (Geomatikum) 20146 Hamburg |
Raum 314 Tel.: +49 40 42838-5183 Fax: +49 40 42838-5190 E-Mail: klaus.kroencke (at) uni-hamburg.de |
Sprechstunden im WiSe 2020:
virtuell, nach Vereinbarung
About me:
I am an assistant professor in Mathematics at the University of Hamburg. Before I moved to Hamburg, I was a postdoc at the University of Regensburg. I obtained my PhD degree in Mathematics at the University of Potsdam under the supervision of Prof. Dr. Christian Bär, funded by the Max Planck Institute for Gravitational Physics. Previously, I did my diploma studies in Mathematics at the University of Vienna.
In the summer term 2020, I am on leave. I am a substitute professor at the University of Tübingen.
My research interests revolve around differential geometry, geometric analysis, partial differential equations and general relativity. More precisely, I am interested in special geometric structures (Einstein metrics and Ricci solitons), their stability and the structure of their moduli spaces. Moreover, I am interested in geometric flows (in particular Ricci flow) and nonlinear stability problems in general relativity.
Teaching:
SS 2020 | Vorlesung: Analysis I (Universität Tübingen) |
WS 2019 | No teaching (research semester) |
SS 2019 | Lecture: Ricci flow |
SS 2019 | Seminar: Lorentzian geometry |
WS 2018 | Lecture: Advanced differential geometry |
SS 2018 | Vorlesung: Differentialgeometrie |
WS 2017 | Vorlesung: Partielle Differentialgleichungen |
SS 2017 | Research Seminar: Differential geometry (with Stefan Suhr) |
SS 2017 | Seminar: Elementare Differentialgeometrie |
WS 2016 | Vorlesung: Höhere Analysis |
SS 2016 | Lecture: Ricci flow |
SS 2016 | Seminar: Lorentzgeometrie |
WS 2015 | Lecture: Riemannian geometry |
Seminar:
- Nonlinear wave equations (with Jan Metzger, Potsdam)
Publications:
-
Perelman's Entropies for Manifolds with conical Singularities (with Boris Vertman)
[arXiv]
To appear in: Trans. Amer. Math. Soc. -
Mean curvature flow in asymptotically flat product spacetimes (with Oliver Lindblad Petersen, Felix Lubbe et al)
[Journal, arXiv]
To appear in: J. Geom. Anal. -
Stability of ALE Ricci-flat manifolds under Ricci flow (with Alix Deruelle)
[Journal, arXiv]
To appear in: J. Geom. Anal. -
Stable fixed points of the Einstein flow with positive cosmological constant (with David Fajman)
[Journal, arXiv]
Comm. Anal. Geom. 28 (2020) no. 7, 1533-1576 -
Stability of Einstein metrics under Ricci flow
[Journal, arXiv]
In: Comm. Anal. Geom. 28 (2020) no. 2, 351-394 -
Stable cosmological Kaluza-Klein Spacetimes (with Volker Branding and David Fajman)
[Journal, arXiv]
In: Comm. Math. Phys. 368 (2019) no. 3, 1087-1120 -
Holonomy rigidity for Ricci-flat metrics (with Bernd Ammann, Hartmut Weiß and Frederik Witt) [Journal, arXiv]
In: Math. Z. 291 (2019) no. 1-2, 303-311 -
Stability of Ricci de Turck flow on Singular Spaces (with Boris Vertman)
[Journal, arXiv]
In: Calc. Var. Partial Differ. Equ. 58 (2019) no. 2, 74 -
On the CMC-Einstein-Λ flow (with David Fajman)
[Journal, arXiv]
In: Class. Quantum Grav. 35 (2018) no. 19, 195005 -
Global existence of Dirac-wave maps with curvature term on expanding spacetimes (with Volker Branding)
[Journal, arXiv]
In: Calc. Var. Partial Differ. Equ. 57 (2018) no. 5, 119 -
Stability of sin-cones and cosh-cylinders [Journal, arXiv]
In: Ann. Sc. Norm. Super. Pisa, Cl. Sci. 18 (2018) no. 3, 1155-1187 -
Ricci flow with metric torsion on closed surfaces (with Volker Branding)
[Journal, arXiv]
In: J. Geom. Anal. 27 (2017) no. 3, 2098-2117 -
Stable and unstable Einstein warped products [Journal, arXiv]
In: Trans. Amer. Math. Soc. 369 (2017) no. 9, 6537-6563 -
The Einstein-Λ flow on product manifolds (with David Fajman)
[Journal, arXiv]
In: Class. Quant. Grav. 33 (2016) no. 23, 235018 -
Rigidity and infinitesimal deformability of Ricci solitons
[Journal, arXiv]
In: J. Geom. Anal. 26 (2016) no. 3, 1795-1807 -
Stability and instability of Ricci solitons [Journal, arXiv]
In: Calc. Var. Partial Differ. Equ. 53 (2015) no. 1-2,265-287 -
On the stability of Einstein manifolds
[Journal, arXiv]
In: Ann. Global Anal. Geom. 47 (2015) no. 1-2, 81-98 -
On infinitesimal Einstein deformations
[Journal, arXiv]
In: Differ. Geom. Appl. 38 (2015) 41-57
Preprints:
- Spectra, stability and rigidity of sine-cones [arXiv]
- Lp-stability and positive scalar curvature rigidity of Ricci-flat ALE manifolds (with Oliver Lindblad Petersen) [arXiv]
- Long-time estimates for heat flows on ALE manifolds (with Oliver Lindblad Petersen) [arXiv]
- Bounded Ricci Curvature and Positive Scalar Curvature under Singular Ricci de Turck Flow (with Tobias Marxen and Boris Vertman) [arXiv]
- Construction of initial data sets for Lorentzian manifolds with lightlike parallel spinors (with Bernd Ammann and Olaf Müller) [arXiv]
Conference proceedings:
-
A survey on the Ricci flow on singular spaces (with Boris Vertman) [Cambrige]
O. Dearricott et al. (eds.) Differential Geometry in the Large, Cambridge University Press. 463, 118-140 -
Stability of ALE Ricci-flat manifolds under Ricci flow [MFO]
In: Oberwolfach Reports 14 (2017) no. 3, 2256-2258 -
Variational Stability and Rigidity of compact Einstein Manifolds [Springerlink]
F. Finster et al. (eds.) Quantum Mathematical Physics. A Bridge between Mathematics and Physics, 497-513, Springer, 2016 -
Stability and instability of Ricci solitons [MFO]
In: Oberwolfach Reports 11 (2014) no. 3, 2017-2019 -
Scars of periodic orbits [MFO]
In: Oberwolfach Reports 8 (2011) no. 4, 2823–2825
Books:
-
Geometric Flows and the Geometry of Space-time [Springerlink]
Editors: Vicente Cortés, Klaus Kröncke, Jan Louis
Tutorials, Schools, and Workshops in the Mathematical Sciences, Birkhäuser, 2018
Theses:
- Stability of Einstein Manifolds [OPUS]
Doctoral thesis, University of Potsdam, 2013 - Comparison theorems in Riemannian geometry [E-theses]
Diploma thesis, University of Vienna, 2010
Events:
-
Wave equations and Fourier integral operators on models of an expanding universe
Winter school, Konstanz, January 15-17, 2020
Organizers: Klaus Kröncke (Hamburg), Jan Metzger (Potsdam), Oliver Lindblad Petersen (Hamburg) -
10th Northern German Differential Geometry Day
Hamburg, June 21, 2019
Organizers: Roger Bielawski, Lynn Heller and Knut Smoczyk (Hannover), Vicente Cortés and Klaus Kröncke (Hamburg), Jens Heber and Hartmut Weiß (Kiel) -
Ricci flow, mean curvature flow and related singular flows
Workshop, Hamburg, September 3-6, 2018
Organizers: Klaus Kröncke (Hamburg), Oliver Schnürer (Konstanz), Miles Simon (Magdeburg) and Boris Vertman (Oldenburg) -
9th Northern German Differential Geometry Day
Kiel, June 8, 2018
Organizers: Roger Bielawski, Lynn Heller and Knut Smoczyk (Hannover), Vicente Cortés and Klaus Kröncke (Hamburg), Jens Heber and Hartmut Weiß (Kiel) -
Field equations on Lorentzian space-times
Workshop, Hamburg, March 19-23, 2018
Organizers: Vicente Cortés, Sari Ghanem and Klaus Kröncke (Hamburg) -
Geometric evolution equations
Winter school, Konstanz, February 5-9, 2018
Organizers: Klaus Kröncke (Hamburg), Oliver Schnürer (Konstanz), Miles Simon (Magdeburg) and Boris Vertman (Oldenburg) -
8th Northern German Differential Geometry Day
Hannover, June 30, 2017
Organizers: Roger Bielawski and Knut Smoczyk (Hannover), Vicente Cortés and Klaus Kröncke (Hamburg), Jens Heber and Hartmut Weiß (Kiel) -
Geometric Flows and the Geometry of Space-time
Summer School and Workshop, Hamburg, September 19-23, 2016
Organizers: Vicente Cortés, Klaus Kröncke and Jan Louis (Hamburg) -
7th Northern German Differential Geometry Day
Hamburg, June 10, 2016
Organizers: Roger Bielawski and Knut Smoczyk (Hannover), Vicente Cortés and Klaus Kröncke (Hamburg), Jens Heber and Hartmut Weiß (Kiel)
Third-party projects:
-
Stability and instability of Einstein manifolds with prescribed asymptotic geometry
Project within the framework of the SPP 2026 Geometry at infinity - Differential geometry and Supersymmetry
Project within the Graduiertenkolleg 1670 Mathematics inspired by string theory and quantum field theory
Spokesperson: Christoph Schweigert
Selected seminar and conference talks:
- Dec 17, 2020, Seminar on Differential Geometry, University of Potsdam
- Oct 21, 2020, Colloquim on Analysis, University of Freiburg
- Aug 15, 2020, Virtual conference on Ricci and Scalar Curvature
- Jul 03, 2020, 3rd FHST Meeting on Geometric Analysis, University of Tübingen
- Jun 22, 2020, Seminar on Differential Geometry, University of Regensburg
- Jun 04, 2020, Seminar on Geometric Analysis, City University of New York
- May 18, 2020, Differential Geometry Seminar, University of Münster
- Apr 23, 2020, Seminar on Geometric Analysis, University of Tübingen
- Sep 25, 2019, The first Geometry Conference for Friendship of Japan and Germany, Chuo University, Tokyo
- Sep 12, 2019, Seminar on General Relativity, Geometry and Analysis, Mittag-Leffler Institute, Stockholm
- Jun 18, 2019, Conference on Harmonic Analysis and Spectral Theory, Technion Haifa
- Apr 3, 2019, Conference on Geometry at Infinity, University of Münster
- Feb 15, 2019, Workshop on Differential Geometry in the Large, Matrix Institute, Melbourne
- Feb 8, 2019, Conference on Differential Geometry in the Large, Matrix Institute, Melbourne
- Oct 12, 2018, Conference on Stability Phenomena in Geometry and Mathematical Physics, HU Berlin
- Sep 21, 2018, Conference on Geometric Analysis and Mathematical Physics, University of Oldenburg
- Sep 18, 2018, Conference on Analytical Problems in Conformal Geometry, University of Regensburg
- May 24, 2018, Seminar on Analysis, University of Warwick
- May 8, 2018, Conference on Geometric Analysis and Mathematical Physics, Mittag-Leffler Institute, Stockholm
- Apr 23, 2018, Differential Geometry Seminar, University of Münster
- Mar 5, 2018, Workshop on Geometric Evolution Equations, University of Regensburg
- Mar 2, 2018, Seminar on Global Analysis, University of Regensburg
- Jan 25, 2018, Seminar on Differential Geometry, University of Potsdam
- Dec 22, 2017, 6th Christmas colloquium, Technical University of Vienna
- Nov 24, 2017, Seminar on Nonlinear Analysis, University of Vienna
- Oct 9-13, 2017, Summer school on Geometric Analysis on Noncompact Manifolds, University of Copenhagen
- Oct 2, 2017, Geometry and Topology Seminar, McMaster University
- Sep 29, 2017, Seminar on Geometric Analysis, Rutgers University
- Sep 28, 2017, Seminar on Geometric Analysis, City University of New York
- Sep 26, 2017, Seminar on Geometric Analysis, University of Maryland
- Sep 14, 2017, Postdoctoral Seminar, Fields Institute, Toronto
- Sep 6, 2017, Geometric Analysis Colloquium, Fields Institute, Toronto
- Aug 9, 2017, Workshop on Positive Scalar Curvature, Oberwolfach
- May 16, 2017, Seminar on Analysis and Theoretical Physics, University of Hannover
- Apr 20, 2017, Analysis Seminar, University of Oldenburg
- Feb 16, 2017, 7th European Relativity Seminar, University of Bremen
- Feb 9, 2017, Colloquium of the Graduiertenkolleg, University of Regensburg
- Dec 9, 2016, Seminar on PDE and Dynamical Systems, University of Hamburg
- Jul 7, 2016, Seminar on Differential Geometry and Analysis, University of Hannover
- Jun 23, 2016, Geometric Analysis Seminar, AEI Potsdam
- Jun 10, 2016, 7th Northern German Differential Geometry Day, University of Hamburg
- Feb 9, 2016, Seminar on Riemannian Geometry, MSRI Berkeley
- Dec 21, 2015, Seminar on Special Holonomy, University of Regensburg
- Nov 24, 2015, Colloquium in Pure Mathematics, University of Hamburg
- Sep 30, 2015, Seminar on Dirac Operators, University Paris-Sud
- Sep 22, 2015, Jahrestagung der DMV, Hamburg
- Aug 19, 2015, Geometric Analysis Seminar, MPIM Bonn
- May 19, 2015, Geometry Seminar, University of Munich
- Feb 27, 2015, 5th European Relativity Seminar, Hungarian Academy of Sciences, Budapest
- Jan 23, 2015, Brussels-London geometry seminar, University of Brussels
- Jan 14, 2015, Geometry Seminar, University of Kiel
- Nov 25, 2014, Geometry and Topology Seminar, University of Stuttgart
- Aug 7, 2014, Workshop on Positive Scalar Curvature, Oberwolfach
- May 28, 2014, Geometry and Physics Seminar, University of Vienna
- May 13, 2014, Workshop on Kähler Geometry and Geometric Analysis, University College Cork
- March 27, 2014, Workshop on Geometric and Singular Analysis, University of Potsdam
- Feb 28, 2014, 4th European Relativity Seminar, ESI Vienna
- Dec 5, 2013, Topics in Geometric Analysis Seminar, AEI Potsdam
- Nov 6, 2013, Global Analysis and Geometry Seminar, University of Regensburg
- Nov 4, 2013, Differential Geometry Seminar, University of Münster
- Apr 7, 2013, Global Analysis Seminar, University of Bonn
- Mar 8, 2013, Gravitational Physics Seminar, University of Vienna
- Jan 28, 2013, Geometric Analysis Seminar, AEI Potsdam