Klaus Kroencke
Fachbereich Mathematik
Bereich AD
Bundesstraße 55 (Geomatikum)
20146 Hamburg
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Raum 314
Tel.: +49 40 42838-5183
Fax: +49 40 42838-5190
E-Mail:
klaus.kroencke (at) uni-hamburg.de
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Sprechstunden im SoSe 2018:
Di 10-11 Uhr und nach Vereinbarung per E-Mail
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.
My research interests revolve around differential geometry, global
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.
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Holonomy rigidity for Ricci-flat metrics (with Bernd Ammann, Hartmut Weiß and Frederik Witt) [arXiv]
To appear in: Math. Z.
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Stable fixed points of the Einstein flow with positive cosmological constant (with David Fajman)
[arXiv]
To appear in: Comm. Anal. Geom.
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Stability of Einstein metrics under Ricci flow
[arXiv]
To appear in: Comm. Anal. Geom.
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Stability of sin-cones and cosh-cylinders [arXiv]
To appear in: Ann. Sc. Norm. Super. Pisa, Cl. Sci.
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Ricci flow with metric torsion on closed surfaces (with Volker Branding)
[Journal, arXiv]
In: J. Geom. Anal. 27 (2017) no. 3, 2098-2117
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Stable and unstable Einstein warped products [Journal, arXiv]
In: Trans. Amer. Math. Soc. 369 (2017) no. 9, 6537-6563
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The Einstein-Λ flow on product manifolds (with David Fajman)
[Journal, arXiv]
In: Class. Quant. Grav. 33 (2016) no. 23, 235018
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Rigidity and infinitesimal deformability of Ricci solitons
[Journal, arXiv]
In: J. Geom. Anal. 26 (2016) no. 3, 1795-1807
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Stability and instability of Ricci solitons [Journal, arXiv]
In: Calc. Var. Partial Differ. Equ. 53 (2015) no. 1-2,265-287
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On the stability of Einstein manifolds
[Journal, arXiv]
In: Ann. Global Anal. Geom. 47 (2015) no. 1-2, 81-98
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On infinitesimal Einstein deformations
[Journal, arXiv]
In: Differ. Geom. Appl. 38 (2015) 41-57
Preprints:
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Stable cosmological Kaluza-Klein Spacetimes (with Volker Branding and David Fajman)
[arXiv]
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Stability of Ricci de Turck flow on Singular Spaces (with Boris Vertman)
[arXiv]
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Global existence of wave maps and some generalizations on expanding spacetimes (with Volker Branding)
[arXiv]
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Stability of ALE Ricci-flat manifolds under Ricci flow (with Alix Deruelle)
[arXiv]
Conference proceedings:
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Stability of ALE Ricci-flat manifolds under Ricci flow [MFO]
To appear in: Oberwolfach Reports
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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
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Stability and instability of Ricci solitons [MFO]
In: Oberwolfach Reports 11 (2014) no. 3, 2017-2019
- Stability of Einstein Manifolds [OPUS]
Doctoral thesis, University of Potsdam, 2013
- Comparison theorems in Riemannian geometry [E-theses]
Diploma thesis, University of Vienna, 2010
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Field equations on Lorentzian space-times
Workshop, Hamburg, March 19-23, 2018
Organizers: Vicente Cortés, Sari Ghanem and Klaus Kröncke
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Geometric evolution equations
Winter school, Konstanz, February 5-9, 2018
Organizers: Klaus Kröncke, Miles Simon, Oliver Schnürer and Boris Vertman
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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)
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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
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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)
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Stability and instability of Einstein manifolds with prescribed asymptotic geometry
Project within the framework of the SPP 2026 Geometry at infinity
Selected seminar and conference talks:
- April 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
- August 9, 2017, Workshop on Positive Scalar Curvature, Oberwolfach
- May 16, 2017, Seminar on Analysis and Theoretical Physics, University of Hannover
- April 20, 2017, Analysis Seminar, University of Oldenburg
- February 16, 2017, 7th European Relativity Seminar, University of Bremen
- February 9, 2017, Colloquium of the Graduiertenkolleg, University of Regensburg
- December 9, 2016, Seminar on PDE and Dynamical Systems, University of Hamburg
- July 7, 2016, Seminar on Differential Geometry and Analysis, University of Hannover
- June 23, 2016, Geometric Analysis Seminar, AEI Potsdam
- June 10, 2016, 7th Northern German Differential Geometry Day, University of Hamburg
- February 9, 2016, Seminar on Riemannian Geometry, MSRI Berkeley
- December 21, 2015, Seminar on Special Holonomy, University of Regensburg
- November 24, 2015, Colloquium in Pure Mathematics, University of Hamburg
- September 30, 2015, Seminar on Dirac Operators, University Paris-Sud
- September 22, 2015, Jahrestagung der DMV, Hamburg
- August 19, 2015, Geometric Analysis Seminar, MPIM Bonn
- May 19, 2015, Geometry Seminar, University of Munich
- February 27, 2015, 5th European Relativity Seminar, Hungarian Academy of Sciences, Budapest
- January 23, 2015, Brussels-London geometry seminar, University of Brussels
- January 14, 2015, Geometry Seminar, University of Kiel
- November 25, 2014, Geometry and Topology Seminar, University of Stuttgart
- August 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
- February 28, 2014, 4th European Relativity Seminar, ESI Vienna
- December 5, 2013, Topics in Geometric Analysis Seminar, AEI Potsdam
- November 6, 2013, Global Analysis and Geometry Seminar, University of Regensburg
- November 4, 2013, Differential Geometry Seminar, University of Münster
- April 7, 2013, Global Analysis Seminar, University of Bonn
- March 8, 2013, Gravitational Physics Seminar, University of Vienna
- January 28, 2013, Geometric Analysis Seminar, AEI Potsdam
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