Klaus Kroencke

Sprechstunden im WiSe 2018:
Mi 13-14 Uhr und nach Vereinbarung per E-Mail

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.

Positions:

A PhD position under my supervision is avaiable, starting from Oct 1st or later. The announcement is avaiable in german and english. The deadline is Aug 31. If you have questions regarding this announcement, feel free to contact me.

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:

• 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:

• 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

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:

• 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