Thomas Leistner

Juniorprofessor am Bereich Analysis und Differentialgeometrie (AD)
Fachbereich Mathematik der Universität Hamburg
Bundesstrasse 55, 20146 Hamburg, Germany

Phone:  +49 (0)40 428385147, Fax: +49 40 42838 5190, Room: Geomatikum 222
E-mail: leistner (at) math (dot) uni-hamburg (dot) de

Mitglied im Zentrum für Mathematische Physik und im SFB 676 "Particles, Strings and the Early Universe: the Structure of Matter and Space-Time" im Teilprojekt  A6: "Mathematical Aspects of String Compactification".

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 Teaching

Sommersemester 2009:

• Mathematik 2 für Studierende der Physik und Übungen
• Kolloquium des ZMP
  

Wintersemester 2008/09:

• Mathematik I für Studierende der Physik und Übungen
• Kolloquium des ZMP 

Teaching in previous years

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Research

Preprints, Publications and Theses:

• Half flat structures and special holonomy (with V. V. Cortés, L. Schäfer, and F. Schulte-Hengesbach), arxiv:0907.122 , 40 pages.
  
• Conformal structures with $G_{2(2)}$-ambient metrics (with P. Nurowski), preprint at arxiv:0904.0186 , 13 pages.  
  
• Ambient metrics for n-dimensional pp-waves (with P. Nurowski), preprint at arXiv:0810.2903, 17 pages.      
  
• Connected subgroups of SO(2,n) acting irreducibly on $\R^{2,n}$ (with A. J. Di Scala), to appear in Israel Journal of Mathematics, preprint available as ESI preprint no. 2033, 22 pages.  
• Cones over pseudo-Riemannian manifolds and their holonomy (with D. V. Alekseevsky, V. Cortés, and A. Galaev), to appear in Crelle's Journal,  preprint available as ESI preprint no. 1939, 47 pages.
  
• Holonomy groups of Lorentzian manifolds: classification, examples and applications. (with Anton Galaev), in  Recent Developments in Pseudo-Riemannian Geometry, ESI-Series on Mathematics and Physics,  European Mathematical Society, 2008.  
• Recent development in pseudo-Riemannian holonomy theory (with Anton Galaev), 2006, to appear in Handbook of Pseudo-Riemannian Geometry, IRMA Lectures in Mathematics and Theoretical Physics.   
  
• Irreducibly acting subgroups of $Gl(n,\rr)$ (with Antonio J. Di Scala and Thomas Neukirchner), 2005, to appear in the Handbook of Pseudo-Riemannian Geometry, IRMA Lectures in Mathematics and Theoretical Physics, math.DG/0507047.    
  
• Higher symmetries of the square of the Laplacian (with Michael Eastwood), in: Symmetries and Overdetermined Systems of Partial Differential Equations,  Vol. 144  of IMA Volumes  in Mathematics and Its Applications, 2008: 319-338, link to toc, also at  math.DG/0610610 . 
• Ambient connections realising conformal Tractor holonomy (with Stuart Armstrong), Monatshefte fuer Mathematik, 152 (2007), no. 4: 265-282, journal link.  
  
• On the classification of Lorentzian holonomy groups, Journal of Differential Geometry, 76, no. 3: 423-484, journal link.
  
• Screen bundles of Lorentzian manifolds and some generalisations of pp-waves, Journal of Geometry and Physics, 56 (2006), no. 10: 2117 -- 2134,  journal link  (also as  math.DG/0507048).
• Conformal holonomy of C-spaces, Ricci-flat, and Lorentzian manifolds, Differential Geometry and its Applications, 24 (2006), no. 5: 458 -- 478, journal link, also at math.DG/0501239).
  
• Holonomy and Parallel Spinors in Lorentzian Geometry, Dissertation, Humboldt-Universität zu Berlin, 2003, published in Logos-Verlag Berlin, 2004.
  
• Towards a classification of Lorentzian holonomy groups. Part II: Semismple, non-simple weak-Berger algebras, 2003,  math.DG/0309274.
• Towards a classification of Lorentzian holonomy groups, 2003, math.DG/0305139.
• Berger algebras, weak-Berger algebras and Lorentzian holonomy, Sfb 288-preprint no. 567, 2002: ftp://ftp-sfb288.math.tu-berlin.de/pub/Preprints/preprint567.ps.gz.
• Lorentzian manifolds with special holonomy and parallel spinors, in: The proceedings of the 21st winter school "Geometry and Physics", Srni, January 13-20, 2001, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Nr. 69, pp. 131-159, 2002 (This is an extended version of the SFB 288 preprint no. 468 wit h some additional results.)
• Das Huygenssche Prinzip fuer den Diracoperator auf Lorentzmannigfaltigkeiten (The Huygens priciple for the Dirac operator on Lorentzian manifolds), diploma thesis, Humboldt University Berlin, 1999, zipped ps-file.

Recent talks:

• Cones over pseudo-Riemannian manifolds and their holonomy, talk given at: Seminario de Xeometria e Topoloxıa, Universidade de Santiago de Compostela, July 18, 2007, at
  Forschungsseminar Differentialgeometrie, Potsdam University, July 19, 2007, at the Pure Mathematics Colloquium of the Department of Mathematics, Hamurg University, February 5, 2008, and at the Seminar for Differential Geometry, Mathematics Institute, Humboldt University, February 13, 2008.
  
• Recent developments in pseudo-Riemannian holonomy theory: classification, examples, and applications, invited talk at the  Symposium on Differential Geometry, Annual conference of the Deutsche Mathematiker Vereinigung (Association of German Mathematicians), Berlin, March 25 – March 30, 2007.
  
• Holonomy groups of Lorentzian manifolds, invited lecture at the IVth International Meeting on Lorentzian Geometry, Santiago de Compostela, February 5 – 8, 2007.
  
• Some results about conformal Tractor holonomy, Humboldt University Berlin,   Seminar on Differential Geometry, abstract.    
  
• Ambient connections realising conformal Tractor holonomy,  Poster at the IMA 2006 Summer programm Symmetries and Overdetermined Systems of Partial Differential Equations, July 15 - August 4, 2006, University of Minnesota. 
  
• Conformal holonomy of Lorentzian manifolds, 08/04/2005, IGA, University of Adelaide, pdf-file of the slides.
• Transitivity of Lorentzian holonomy systems and some generalisations of pp-waves, Workshop on  Differential Geometry and Mathematical Physics, Humboldt University of Berlin,  July 14 - 16, 2004.
• Lorentzian holonomy groups (with application to parallel spinors). Different versions of this talk I gave at several occasions: at the <>Black Sea EDGE-Workshop on Differential Geometry,  Albena, Bulgaria, July 7 - 13, 2003 , at the Workshop on Differential Geometry:  Transformation Groups, Holonomy and Spinors in  Pseudo-Riemannian Geometry, Humboldt University of Berlin,  September 23 - 25, 2003,  at the  IGA seminar<>, at the Colloquium of the Priority programm Global Differential Geometry, Leipzig 23.-25. Juli 2004, and at the 48th Annual Meeting of the Australian Mathematical Society, Melbourne,  September 28 - October 1, 2004. Here is the most comprehensive version of it.
  

Recent and upcoming conferences:

• 2006 IMA Summer Programme: Symmetries and Overdetermined Systems of Partial Differential Equations, July 17 - August 4, 2006,  Minneapolis;
• IV International Meeting on Lorentzian Geometry, Santiago de Compostela, February 5 - 8, 2007;
• 2007 Annual Meeting of the  German Mathematical Society, March 25 - 30, 2007, Berlin;
• 2007 Midwest Geometry Conference, to be held in the honour of Tom P. Branson (1953 -2006), May 18 - 20, 2007, Iowa City.
  
• Oberwolfach Seminar Recent Developments in Conformal Differential Geometry,  Mathematisches Forschungsinstitut Oberwolfach, November 18th - November 24th, 2007.
• Workshop "Holonomy Groups and Applications in String Theory", Hamburg University, July, 14-18, 2008.
• Lorentzian Geometry. Analysis and Geometry of pseudo-Riemannian Manifolds , Alfried Krupp Kolleg Greifswald, July 20-22, 2009.

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Last update:  April 01, 2009 by T. Leistner