Fachbereich Mathematik 
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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 2017:
Di 10-11 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.

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.


Teaching:

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


Publications:

  • Stability of sin-cones and cosh-cylinders [arXiv]
    To appear in: Ann. Sc. Norm. Super. Pisa, Cl. Sci.
  • 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:

  • Global existence of wave maps and some generalizations on expanding spacetimes (with Volker Branding) [arXiv]
  • Stability of ALE Ricci-flat manifolds under Ricci flow (with Alix Deruelle) [arXiv]
  • Holonomy rigidity for Ricci-flat metrics (with Bernd Ammann, Hartmut Weiß and Frederik Witt) [arXiv]
  • Stable fixed points of the Einstein flow with positive cosmological constant (with David Fajman) [arXiv]
  • Ricci flow, Einstein metrics and the Yamabe invariant [arXiv]

Conference proceedings:

  • Stability of ALE Ricci-flat manifolds under Ricci flow
    To appear in: Oberwolfach Reports
  • 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

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:

  • 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
  • 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)


Selected seminar and conference talks:

  • 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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