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Klaus Kroencke
Fachbereich Mathematik Bereich AD Bundesstraße 55 (Geomatikum) 20146 Hamburg 
Raum 314 Tel.: +49 40 428385183 Fax: +49 40 428385190 EMail: klaus.kroencke (at) unihamburg.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 Ricciflat 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, 15331576 
Stability of Einstein metrics under Ricci flow
[Journal, arXiv]
In: Comm. Anal. Geom. 28 (2020) no. 2, 351394 
Stable cosmological KaluzaKlein Spacetimes (with Volker Branding and David Fajman)
[Journal, arXiv]
In: Comm. Math. Phys. 368 (2019) no. 3, 10871120 
Holonomy rigidity for Ricciflat metrics (with Bernd Ammann, Hartmut Weiß and Frederik Witt) [Journal, arXiv]
In: Math. Z. 291 (2019) no. 12, 303311 
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 CMCEinsteinΛ flow (with David Fajman)
[Journal, arXiv]
In: Class. Quantum Grav. 35 (2018) no. 19, 195005 
Global existence of Diracwave 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 sincones and coshcylinders [Journal, arXiv]
In: Ann. Sc. Norm. Super. Pisa, Cl. Sci. 18 (2018) no. 3, 11551187 
Ricci flow with metric torsion on closed surfaces (with Volker Branding)
[Journal, arXiv]
In: J. Geom. Anal. 27 (2017) no. 3, 20982117 
Stable and unstable Einstein warped products [Journal, arXiv]
In: Trans. Amer. Math. Soc. 369 (2017) no. 9, 65376563 
The EinsteinΛ 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, 17951807 
Stability and instability of Ricci solitons [Journal, arXiv]
In: Calc. Var. Partial Differ. Equ. 53 (2015) no. 12,265287 
On the stability of Einstein manifolds
[Journal, arXiv]
In: Ann. Global Anal. Geom. 47 (2015) no. 12, 8198 
On infinitesimal Einstein deformations
[Journal, arXiv]
In: Differ. Geom. Appl. 38 (2015) 4157
Preprints:
 Spectra, stability and rigidity of sinecones [arXiv]
 L^{p}stability and positive scalar curvature rigidity of Ricciflat ALE manifolds (with Oliver Lindblad Petersen) [arXiv]
 Longtime 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, 118140 
Stability of ALE Ricciflat manifolds under Ricci flow [MFO]
In: Oberwolfach Reports 14 (2017) no. 3, 22562258 
Variational Stability and Rigidity of compact Einstein Manifolds [Springerlink]
F. Finster et al. (eds.) Quantum Mathematical Physics. A Bridge between Mathematics and Physics, 497513, Springer, 2016 
Stability and instability of Ricci solitons [MFO]
In: Oberwolfach Reports 11 (2014) no. 3, 20172019 
Scars of periodic orbits [MFO]
In: Oberwolfach Reports 8 (2011) no. 4, 2823–2825
Books:

Geometric Flows and the Geometry of Spacetime [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 [Etheses]
Diploma thesis, University of Vienna, 2010
Events:

Wave equations and Fourier integral operators on models of an expanding universe
Winter school, Konstanz, January 1517, 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 36, 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 spacetimes
Workshop, Hamburg, March 1923, 2018
Organizers: Vicente Cortés, Sari Ghanem and Klaus Kröncke (Hamburg) 
Geometric evolution equations
Winter school, Konstanz, February 59, 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 Spacetime
Summer School and Workshop, Hamburg, September 1923, 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)
Thirdparty 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, MittagLeffler 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, MittagLeffler 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 913, 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 ParisSud
 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, BrusselsLondon 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