Klaus Kroencke

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:

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.
• Stable fixed points of the Einstein flow with positive cosmological constant (with David Fajman) [arXiv]
  To appear in: Comm. Anal. Geom. 28 (2020)
• 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.
• Stability of Einstein metrics under Ricci flow [Journal, arXiv]
  To appear 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]
• L^p-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