Thomas Leistner

Associate Professor Thomas Leistner

Associate Professor

School of Mathematical Sciences

Faculty of Engineering, Computer and Mathematical Sciences

Eligible to supervise Masters and PhD - email supervisor to discuss availability.


I am Associate Professor in Pure Mathematics. I did my PhD at Humboldt-University Berlin, held postdoc positions at Berlin and Adelaide, and worked as a Assistant Professor at the University of Hamburg before joining the University of Adelaide.
My research lies in differential geometry, which is an area of pure mathematics that deals with curved spaces (and space-times) and has applications in mathematical physics, in particular in general relativity and string theory.

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 and holonomy groups. Some of my research has applications in mathematical physics, in particular in general relativity and string theory.

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  • Journals

    Year Citation
    2020 Anderson, I. M., Leistner, T., & Nurowski, P. (2020). Explicit ambient metrics and holonomy. Journal of Differential Geometry, 114(2), 193-242.
    DOI
    2020 Francis-Staite, K., & Leistner, T. (2020). Conformal properties of indefinite bi-invariant metrics. Transformation Groups, OnlinePubl(3), 1-34.
    DOI
    2019 Gover, A., & Leistner, T. (2019). Invariant prolongation of the Killing tensor equation. Annali di Matematica Pura ed Applicata, 198(1), 307-334.
    DOI Scopus2 WoS2
    2017 Leistner, T., & Lischewski, A. (2017). Hyperbolic Evolution Equations, Lorentzian Holonomy, and Riemannian Generalised Killing Spinors. Journal of Geometric Analysis, 29(1), 33-82.
    DOI Scopus1 WoS1
    2017 Leistner, T., & Lischewski, A. (2017). The ambient obstruction tensor and conformal holonomy. Pacific Journal of Mathematics, 290(2), 403-436.
    DOI
    2017 Leistner, T., Nurowski, P., & Sagerschnig, K. (2017). New relations between G₂ geometries in dimensions 5 and 7. International Journal of Mathematics, 28(13), 1750094-1-1750094-46.
    DOI Scopus4 WoS4
    2016 Globke, W., & Leistner, T. (2016). Locally homogeneous pp-waves. Journal of Geometry and Physics, 108, 83-101.
    DOI
    2016 Baum, H., Leistner, T., & Lischewski, A. (2016). Cauchy problems for Lorentzian manifolds with special holonomy. Differential Geometry and Its Applications, 45, 43-66.
    DOI Scopus3 WoS3
    2016 Leistner, T., & Schliebner, D. (2016). Completeness of compact Lorentzian manifolds with abelian holonomy. Mathematische Annalen, 364(3-4), 1469-1503.
    DOI Scopus11 WoS10
    2014 Alt, J., Di Scala, A., & Leistner, T. (2014). Conformal holonomy, symmetric spaces, and skew symmetric torsion. Differential Geometry and Its Applications, 33(Suppl.), 4-43.
    DOI Scopus3 WoS3
    2014 Baum, H., Lärz, K., & Leistner, T. (2014). On the full holonomy group of Lorentzian manifolds. Mathematische Zeitschrift, 277(3-4), 797-828.
    DOI Scopus10 WoS11
    2012 Leistner, T., & Nurowski, P. (2012). Ambient metrics with exceptional holonomy. Scuola Normale Superiore di Pisa. Annali. Classe di Scienze, 11(2), 407-436.
    DOI Scopus17 WoS17
    2012 Leistner, T., & Nurowski, P. (2012). Conformal pure radiation with parallel rays. Classical and Quantum Gravity, 29(5), 055007-1-055007-15.
    DOI Scopus13 WoS12
    2011 Di Scala, A., & Leistner, T. (2011). Connected subgroups of SO(2,n) acting irreducibly on ℝ²,ⁿ. Israel Journal of Mathematics, 182(1), 103-121.
    DOI Scopus11 WoS10
    2011 Cortes, V., Leistner, T., Schafer, L., & Schulte-Hengesbach, F. (2011). Half-flat structures and special holonomy. Proceedings of the London Mathematical Society, 102(1), 113-158.
    DOI Scopus33 WoS34
    2010 Galaev, A., & Leistner, T. (2010). On the local structure of Lorentzian Einstein manifolds with parallel distribution of null lines. Classical and Quantum Gravity, 27(22), 1-16.
    DOI Scopus13 WoS11
    2010 Leistner, T., & Nurowski, P. (2010). Ambient metrics for n-dimensional pp-waves. Communications in Mathematical Physics, 296(3), 881-898.
    DOI Scopus21 WoS21
    2009 Alekseevsky, D., Cortes, V., Galaev, A., & Leistner, T. (2009). Cones over pseudo-Riemannian manifolds and their holonomy. Journal fur die Reine und Angewandte Mathematik, 635(635), 23-69.
    DOI Scopus43 WoS44
    2007 Leistner, T. (2007). On the classification of Lorentzian holonomy groups. Journal of Differential Geometry, 76(3), 423-484.
    Scopus53 WoS53
    2007 Armstrong, S., & Leistner, T. (2007). Ambient connections realising conformal Tractor holonomy. Monatshefte fur Mathematik, 152(4), 265-282.
    DOI Scopus6 WoS5
    2006 Leistner, T. (2006). Conformal holonomy of C-spaces, Ricci-flat, and Lorentzian manifolds. Differential Geometry and its Applications, 24(5), 458-478.
    DOI Scopus32 WoS34
    2006 Leistner, T. (2006). Screen bundles of Lorentzian manifolds and some generalisations of pp-waves. Journal of Geometry and Physics, 56(10), 2117-2134.
    DOI Scopus20 WoS24
    Leistner, T. (n.d.). Towards a classification of Lorentzian holonomy groups. Part II:
    Semisimple, non-simple weak-Berger algebras. J. Differential Geom. 76 (2007), no. 3, 423-484.
  • Books

    Year Citation
    2020 Dearricott, O., Tuschmann, W., Nikolayevsky, Y., Leistner, T., & Crowley, D. (2020). Differential Geometry in the Large. O. Dearricott, W. Tuschmann, Y. Nikolayevsky, T. Leistner, & D. Crowley (Eds.), Cambridge University Press.
    2004 Leistner, T. (2004). Holonomy and Parallel Spinors in Lorentzian Geometry. Berlin: Logos Verlag.
  • Book Chapters

    Year Citation
    2018 Leistner, T., & Baum, H. (2018). Lorentzian Geometry: Holonomy, Spinors, and Cauchy Problems. In V. Cortés, K. Kröncke, & J. Louis (Eds.), Geometric Flows and the Geometry of Space-time (pp. 1-76). Switzerland: Birkhäuser.
    DOI
    2010 Galaev, A., & Leistner, T. (2010). Recent developments in pseudo-Riemannian holonomy theory. In Handbook of Pseudo-Riemannian Geometry and Supersymmetry (pp. 581-627). Zurich, Switzerland: European Mathematical Society Publishing House.
    DOI
    2010 Di Scala, A., Leistner, T., & Neukirchner, T. (2010). Geometric applications of irreducible representations of Lie groups. In Handbook of Pseudo-Riemannian Geometry and Supersymmetry (pp. 629-651). Zurich, Switzerland: European Mathematical Society Publishing House.
    DOI
    2008 Galaev, A., & Leistner, T. (2008). Holonomy groups of Lorentzian manifolds: classification, examples, and applications. In D. Alekseevsky, & H. Baum (Eds.), Recent Developments in Pseudo-Riemannian Geometry (pp. 53-96). Zurich, Switzerland: European Mathematical Society Publishing House.
  • Conference Papers

    Year Citation
    2008 Eastwood, M., & Leistner, T. (2008). Higher symmetries of the square of the Laplacian. In Proceedings of Symmetries and Overdetermined Systems of Partial Differential Equations Vol. 144 (pp. 319-338). Germany: SPRINGER.
    DOI WoS12
    2002 Leistner, T. (2002). Lorentzian manifolds with special holonomy and parallel spinors. In Supplemento ai Rendiconti del Circolo Matematico di Palermo, II (pp. 131-159). Italy: Springer Italia Srl.
  • Internet Publications

    Year Citation
    2021 Fino, A., Leistner, T., & Taghavi-Chabert, A. (2021). Almost Robinson geometries.
    2020 Fino, A., Leistner, T., & Taghavi-Chabert, A. (2020). Optical geometries.
    2020 Leistner, T. (2020). Semi-Riemannian cones.
    2019 Alekseevsky, D., Cortés, V., & Leistner, T. (2019). Geometry and holonomy of indecomposable cones. http://arxiv.org/abs/1902.02493v1.
    2016 Anderson, I. M., Leistner, T., Lischewski, A., & Nurowski, P. (2016). Conformal Walker metrics and linear Fefferman-Graham equations.

2011-2012: Go8 - DAAD Australia - Germany Joint Research Cooperation Scheme, "Spinor field equations in Lorentzian geometry", joint with Helga Baum (HU-Berlin)

2012-2014: ARC Discovery Project "Holonomy groups in Lorentzian geometry"

2012-2016:  ARC Future Fellowship

2019-2021: ARC Discovery Project "Symmetry and geometric partial differential equations", with Michael Eastwood (Adelaide), Jonathan Kress (UNSW), and Rod Gover (Auckland)

 

Recent teaching:

Mathematics IA

Mathematics IB

Applications of Quantitative Methods in Finance I

Multivariable and Complex Calculus II

Groups and Rings III

Advanced Mathematical Perspectives III

Manifolds, Lie Groups and Lie Algebras (Honours)

Differential Geometry (Honours)

 

 

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  • Current Higher Degree by Research Supervision (University of Adelaide)

    Date Role Research Topic Program Degree Type Student Load Student Name
    2020 Principal Supervisor Homogeneity in Lorentzian Geometry Master of Philosophy Master Full Time Mr Daniel Aaron Franceschinis
    2020 Principal Supervisor Connections in Generalized Geometry Doctor of Philosophy under a Jointly-awarded Degree Agreement with Doctorate Full Time Ms Manasa Manjunatha
    2020 Co-Supervisor The Oka principle in twisted K-theory Doctor of Philosophy Doctorate Full Time Miss Haripriya Sridharan
    2019 Principal Supervisor Geodesic completeness of compact Lorentzian manifolds Master of Philosophy Master Full Time Mr Thomas Jack Munn
    2019 Principal Supervisor Higher Order Symmetries in Lorentzian Geometry Doctor of Philosophy Doctorate Full Time Mr Esteban Federico Costanza
  • Past Higher Degree by Research Supervision (University of Adelaide)

    Date Role Research Topic Program Degree Type Student Load Student Name
    2020 - 2021 Principal Supervisor Approximation of Higher Degree Spectra Results for Twisted Laplace Operators Master of Philosophy Master Full Time Mr Matthias Eduard Fresacher
    2019 - 2021 Co-Supervisor Legendrean and G2 Contact Structures Master of Philosophy Master Full Time Mr Timothy John An Hu Moy
    2019 - 2021 Co-Supervisor Highly symmetric homogeneous Kobayashi-hyperbolic manifolds Doctor of Philosophy Doctorate Full Time Mr Elliot Herrington
    2019 - 2021 Principal Supervisor Conformal group actions on Cahen-Wallach spaces Master of Philosophy Master Full Time Mr Stuart Benjamin Teisseire
    2018 - 2020 Co-Supervisor Theta Functions, Gauss Sums and Modular Forms Master of Philosophy Master Full Time Mr Benjamin Terence Moore
    2017 - 2020 Co-Supervisor Spaces of Holomorphic Immersions of Open Riemann Surfaces into the Complex Plane Master of Philosophy Master Part Time Miss Haripriya Sridharan
    2013 - 2015 Co-Supervisor Einstein and Conformally Einstein Bi-Invariant Semi-Riemannian Metrics Master of Philosophy Master Full Time Dr Kelli Leigh Francis-Staite
  • Position: Associate Professor
  • Phone: 83136401
  • Email: thomas.leistner@adelaide.edu.au
  • Fax: 8313 3696
  • Campus: North Terrace
  • Building: Ingkarni Wardli, floor 6
  • Room: 6 39
  • Org Unit: Mathematical Sciences

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