Associate Professor Thomas Leistner

• Research Interests

  My research lies in differential geometry where I study curved spaces (and space-times), their geometric properties, their symmetries and their relation to interesting differential equations. My research so far has focussed on Lorentzian geometry, conformal geometry, homogeneous spaces, and holonomy groups. Some of my research has applications in mathematical physics, in particular in general relativity and string theory.

  I am happy to supervisor Masters and PhD projects in these areas. Here is a list of current and past potgraduate projects: 

  Current students:
  

  • Lee Ward (MPhil, co-supervisor, principal supervisor Finnur Larusson 
  • Dylan Holland (MPhil, principal supervisor, co-supervisor Mike Estwood
  • Harrison Greven (MPhil, principal supervisor, co-supervisor Mike Eastwood
  • Paawan Nileshkumar Jethva (Mphil, co-supervisor, principal supervisor David Baraglia

  Past students:
  

  • Haripriya Sridharan (PhD, co-supervisor, principal supervisor Finnur Larusson)
    
  • Steven Greenwood (MPhil, principal supervisor, co-supervisor Mike Eastwood, thesis, paper, PhD at  Masaryk University Brno
  • George Savvoudis (MPhil, co-supervisor, principal supervisor Sue Barwick, thesis
  • Federico Costanza (PhD, principal supervisor, co-supervisor Mike Eastwood, paper 1, paper 2, paper 3, thesis
  • Manasa Manjunatha (PhD, with Vicente Cortes, University of Hamburg), thesis   
  • Thomas Munn (MPhil, principal supervisor, co-supervisor Mike Eastwood, thesis, publication, PhD at Lund
  • Matthias Fresacher, (MPhil, principal supervisor, co-supervisors: Nicholas Buchdahl and Peter Hochs), thesis, PhD at University of Western Sydney
  • Elliot Herrington (PhD, co-supervisor, principal supervisor Finnur Larusson), thesis, publication
  • Timothy Moy (MPhil, co-supervisor, principal supervisor Mike EAstwood), thesis, publication, PhD at University of Cambridge
  • Stuart Teisseire (2021, MPhil, principal supervisor, co-supervisor Mike Eastwood) thesis, paper 1, paper 2,  PhD at University of Auckland
  • Benjamin Moore (2020, MPhil, co-supervisor, principal supervisor Mike Eastwood), thesis, publication, PhD at Warwick
  • Haripriya Sridharan (2020, MPhil, co-supervisor, principal supervisor Finnur Larusson), thesis, PhD at Adelaide and Melbourne
  • Daniel Franceschinis (MPhil, principal supervisor, co-supervisor Mike Eastwood)
  • Kelli Francis-Staite (2015, MPhil, co-supervisor, principal supervisor Michael Murray), thesis, publication, PhD at Oxford University as Rhodes Scholar

   

• Research Funding

   

  • ARC Discovery Project "Symmetry and geometric partial differential equations" (2019-2021, with Mike Eastwood, Jonathan Kress, and Rod Gover
  • ARC Future Fellowship (2012-Jan 2016)
  • ARC Discovery Project "Holonomy groups in Lorentzian geometry" (2012-2014)
  • Go8 - DAAD Australia - Germany Joint Research Cooperation Scheme, "Spinor field equations in Lorentzian geometry", joint with Helga Baum (HU-Berlin)

   

• Publications

  
  My publications on MathSciNet, on Scopus, on Google Scholar and preprints on on the arXiv. Preprints

  • Conformal Killing tensors and their Killing scales (with Rod Gover and Jonathan Kress), 35 pages, arxiv:2406.17212
    
  • Lorentzian homogeneous structures with indecomposable holonomy (with Steven Greenwood), 30 pages, arxiv:2404.17470   

  Publications

  • The range of a connection and a Calabi operator for Lorentzian locally symmetric spaces (with Federico Costanza, Michael Eastwood, and Benjamin McMillan), to appear in Asian Journal of Mathematics, 27 pages, arXiv:2302.04480
    
  • A Calabi operator for Riemannian locally symmetric spaces (with Federico Costanza, Michael Eastwood, and Benjamin McMillan), to appear in American Journal of Mathematics, 17 pages, arxiv:2112.00841
  • Compact locally conformally pseudo-Kaehler manifolds with essential conformal transformations (with Vicente Cortes), SIGMA 20(2024), 084, 12 pages, arXiv:2309.11184
  • Fundamental regions for non-isometric group actions (with Stuart Teisseire),Geometriae Dedicata (2024) 218:95, 13 pages, arxiv:2112.11082
  • Killing vector fields on semi-Riemannian product manifolds (with Federico Costanza), to appear in the Matrix Annals, 7 pages, arXiv:2312.00569
  • Conformal transformations of Cahen-Wallach spaces (with Stuart Teisseire), Annales de l'Institute Fourier, 40 pages, arxiv:2201.12958  
  • Almost Robinson geometries (with Anna Fino and Arman Taghavi-Chabert), Letters in Mathematical Physics, Vol. 113, article number 56 (2023), 103 pages, arxiv:2102.05634 
  • Optical geometries (with Anna Fino and Arman Taghavi-Chabert), Annali della Scuola Normale Superiore di Pisa, Classe di Scienze 2025: VOL. XXVI, ISSUE 1, 46 pages, arxiv:2009.10012
  • Completeness of certain compact Lorentzian locally symmetric spaces (with Thomas Munn), Comptes Rendus - Serie Mathematique, Vol 361, (2023), pp. 819-824, arXiv:2211.02380  
  • Semi-Riemannian cones, in Geometry, Lie Theory and Applications: The Abel Symposium 2019, p. 193-222, Abel Symposia volume 16, Springer 2022,  arxiv:2001.07349
  • Semi-Riemannian cones with parallel null planes (with Dmitri Alekseevsky and Vicente Cortes), Developments in Lorentzian Geometry, Proceedings of the 10th International Meeting on Lorentzian Geometry, Springer Proceedings in Mathematics and Statistics, pp. 1-11, arxiv:1902.02493,
  • Geometry and holonomy of indecomposable cones (with Dmitri Alekseevsky and Vicente Cortes), Revista Matematica Iberoamericana (RMI), Vol. 39, no. 3 (2023), pp. 1105-1141, arxiv:1902.02493.
  • Conformal properties of indefinite bi-invariant metrics (with Kelli Francis-Staite),  Transform. Groups 26 (2021), no. 3, 859-892, arxiv:1901.04682 
  • Lorentzian Geometry: Holonomy, Spinors, and Cauchy Problems (with H.Baum), in Geometric Flows and the Geometry of Space-time, edited by Vicente Cortes, Klaus Kroencke and Jan Louis, vol 2 in Tutorials, Schools, and Workshops in the Mathematical Sciences, Birkhaeuser/Springer, 2018, pp 1-76
  • Invariant prolongation of the Killing tensor equation (with A. Rod Gover), Annali di Matematica Pura ed Applicata 198 (2019), Issue 1, pp 307-334, journal link, arxiv:1802.05866 
  • Hyperbolic evolution equations, Lorentzian holonomy, and Riemannian generalised Killing spinors (with A.Lischewski), The Journal of Geometric Analysis, 29, Issue 1, 2019, pp 33-82, journal link,  arXiv:1702.01951 
  • Conformal Walker metrics and linear Fefferman-Graham equations (with I. Anderson,  A. Lischewski, and P. Nurowski), Communications in Analysis and Geometry, Vol 32 (2024), no 3, pp. 693-749, arXiv:1609.02371
  • New relations between $G_2$-geometries in dimensions 5 and 7 (with P. Nurowski and K. Sagerschnig), International Journal of Mathematics 28 (2017), issue 13, 46 pages, journal link, arxiv:1601.03979
  • The ambient obstruction tensor and conformal holonomy (with A. Lischewski), Pacific Journal of Mathematics  290 (2017), no. 2, 403-436, journal link, arXiv:1511.07214
  • Explicit ambient metrics and holonomy (with I.M. Anderson and P. Nurowski), Journal of Differential Geometry, 114 (2), 193-242, journal link, arxiv:1501.00852
  • Cauchy problems for Lorentzian manifolds with special holonomy (with H. Baum and A. Lischewski), Differential Geom. Appl. 45 (April 2016), pp 43-66, journal link, arxiv:1411.3059
  • Locally homogeneous pp-waves (with W. Globke), Journal of Geometry and Physics 108, Oct 2016, 83-101, journal link, arxiv:1410.3572
  • Completeness of compact Lorentzian manifolds with abelian holonomy (with D. Schliebner), Math. Ann. 364 (2016), issue 3, pp 1469-1503, journal link, arxiv:1306.0120.
  • Conformal holonomy, symmetric spaces, and skew symmetric torsion (with J. Alt and A. J. Di Scala), Differential Geom. Appl., Volume 33, Supplement, March 2014, Pages 4-43, arxiv:1208.2191.
  • On the full holonomy group of special Lorentzian manifolds (with Helga Baum and Kordian Laerz),  Math. Z. 277 (2014), no 3-4, 797-828, journal link,  arxiv:1204.5657.
  • Conformal pure radiation with parallel rays (with P. Nurowski), Classical and Quantum Gravity 29 (2012) 055007 (15pp), arxiv.org/abs/1107.1675. 
  • Ambient metrics with exceptional holonomy (with P. Nurowski),  Ann. Sc. Norm. Super. Pisa Cl. Sci., XI, issue 2 (2012), 407-436, journal link, arxiv:0904.0186, 30 pages.
  • Half flat structures and special holonomy (with V. Cortes, L. Schaefer, and F. Schulte-Hengesbach),  Proc.  London Math. Soc.  (3) 102 (2011) 113-158, journal link, arxiv:0907.122. 
  • On the local structure of Lorentzian Einstein manifolds with parallel null line (with A. S Galaev),  Classical Quantum Gravity 27 (2010) 225003 (16pp),  journal link,  arxiv:0912.3400.  
  • Ambient metrics for n-dimensional pp-waves (with P. Nurowski), Comm. Math Phys. 296 (2010), 881-898, journal link, arXiv:0810.2903.  
  • Connected subgroups of SO(2,n) acting irreducibly on $\R^{2,n}$ (with A. J. Di Scala), Israel J. Math. 182 (2011), 103-121, preprint available as arxiv:0806.2586 or as ESI preprint no. 2033     
  • Recent development in pseudo-Riemannian holonomy theory (with Anton Galaev),  Handbook ofPseudo-Riemannian Geometry, IRMA Lectures in Mathematics and Theoretical Physics, 2010, 581-629.   
  • Irreducibly acting subgroups of $Gl(n, r)$ (with Antonio J. Di Scala and Thomas Neukirchner), 2005, Handbook of Pseudo-Riemannian Geometry, IRMA Lectures in Mathematics and Theoretical Physics, 2010, 629-653,  math.DG/0507047.    
    
  • Cones over pseudo-Riemannian manifolds and their holonomy (with D. V. Alekseevsky, V. Cortes, and A. Galaev),  J. reine angew. Math. (Crelle's Journal)  635 (2009), 23-69, journal link, ESI preprint no. 1939.
  • 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, 53-97.
  • 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, also at arXiv:math/0606410.  
  • 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-Universitaet 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 with some additional results.)
  • Das Huygenssche Prinzip fuer den Diracoperator auf Lorentzmannigfaltigkeiten (The Huygens principle for the Dirac operator on Lorentzian manifolds), diploma thesis, Humboldt University Berlin, 1999, zipped ps-file.

   

Entry last updated: Friday, 29 Aug 2025

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