Thomas Leistner

Research Interests

Algebraic and Differential Geometry Algebraic Structures in Mathematical Physics Group Theory and Generalisations Lie Groups, Harmonic and Fourier Analysis Pure Mathematics

Associate Professor Thomas Leistner

Associate Prof/Reader

School of Mathematical Sciences

College of Science

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

I am Associate Professor in Pure Mathematics. I received my PhD from 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.
 
I am the Postgraduate Coordinator in the discipline of Mathematics (for students with surnames starting with G-Z).
 
I organise the Differential Geometry Seminar of the IGA.
 
 

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.

See Research Interests on this page for current and past postgraduate projects.

Date Position Institution name
2020 - ongoing Associate Professor University of Adelaide
2016 - 2019 Senior Lecturer in Pure Mathematics University of Adelaide
2012 - 2016 ARC Future Fellow University of Adelaide
2009 - 2012 Lecturer in Pure Mathematics University of Adelaide
2007 - 2009 Juniorprofessor University of Hamburg
2006 - 2007 Research Associate Humboldt University of Berlin
2003 - 2006 Research Associate University of Adelaide

Language Competency
English Can read, write, speak, understand spoken and peer review
German Can read, write, speak, understand spoken and peer review
Spanish; Castilian Can read, speak and understand spoken

Date Institution name Country Title
2004 Humboldt University of Berlin Germany Doctor rerum naturalium

Year Citation
2025 Leistner, T., & Teisseire, S. (2025). Conformal transformations of Cahen-Wallach spaces. Annales de l'Institut Fourier, 75(5), 2147-2187.
DOI Scopus1 WoS1
2025 Fino, A., Leistner, T., & Taghavi-Chabert, A. (2025). Optical geometries. Annali della Scuola Normale Superiore di Pisa: Classe di Scienze, XXVI(1), 341-396.
DOI
2025 Costanza, F., Eastwood, M., Leistner, T., & McMillan, B. (2025). The range of a connection and a Calabi operator for Lorentzian locally symmetric spaces. Asian Journal of Mathematics, 29(2), 171-200.
DOI
2024 Leistner, T., & Teisseire, S. (2024). Fundamental regions for non-isometric group actions. Geometriae Dedicata, 218(5), 95-1-95-13.
DOI Scopus1 WoS1
2024 Cortés, V., & Leistner, T. (2024). Compact Locally Conformally Pseudo-Kähler Manifolds with Essential Conformal Transformations. Symmetry, Integrability and Geometry: Methods and Applications, 20, 084-1-084-12.
DOI
2024 Anderson, I. M., Leistner, T., Lischewski, A., & Nurowski, P. (2024). Conformal Walker metrics and linear Fefferman-Graham equations. Communications in Analysis and Geometry, 32(3), 693-749.
DOI
2023 Leistner, T., & Munn, T. (2023). Completeness of certain compact Lorentzian locally symmetric spaces. Comptes Rendus Mathematique (Academie des Sciences), 361(1), 819-824.
DOI Scopus2 WoS1
2023 Fino, A., Leistner, T., & Taghavi-Chabert, A. (2023). Almost Robinson geometries. Letters in Mathematical Physics, 113(3), 56-1-56-103.
DOI Scopus5 WoS3
2023 Alekseevsky, D., Cortés, V., & Leistner, T. (2023). Geometry and holonomy of indecomposable cones. Revista Matemática Iberoamericana, 39(3), 1105-1141.
DOI
2020 Anderson, I. M., Leistner, T., & Nurowski, P. (2020). Explicit ambient metrics and holonomy. Journal of Differential Geometry, 114(2), 193-242.
DOI Scopus2 WoS2
2020 Francis-Staite, K., & Leistner, T. (2020). Conformal properties of indefinite bi-invariant metrics. Transformation Groups, 3(3), 1-34.
DOI Scopus1 WoS1
2019 Gover, A., & Leistner, T. (2019). Invariant prolongation of the Killing tensor equation. Annali di Matematica Pura ed Applicata, 198(1), 307-334.
DOI Scopus7 WoS6
2017 Leistner, T., & Lischewski, A. (2017). The ambient obstruction tensor and conformal holonomy. Pacific Journal of Mathematics, 290(2), 403-436.
DOI Scopus3 WoS2
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 Scopus8 WoS9
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 Scopus6 WoS4
2016 Globke, W., & Leistner, T. (2016). Locally homogeneous pp-waves. Journal of Geometry and Physics, 108, 83-101.
DOI Scopus10 WoS12
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 Scopus10 WoS7
2016 Leistner, T., & Schliebner, D. (2016). Completeness of compact Lorentzian manifolds with abelian holonomy. Mathematische Annalen, 364(3-4), 1469-1503.
DOI Scopus32 WoS26
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 Scopus4 WoS4
2014 Baum, H., Lärz, K., & Leistner, T. (2014). On the full holonomy group of Lorentzian manifolds. Mathematische Zeitschrift, 277(3-4), 797-828.
DOI Scopus19 WoS18
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 WoS19
2012 Leistner, T., & Nurowski, P. (2012). Conformal pure radiation with parallel rays. Classical and Quantum Gravity, 29(5), 055007-1-055007-15.
DOI Scopus14 WoS14
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 Scopus17 WoS16
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 Scopus37 WoS37
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 Scopus16 WoS15
2010 Leistner, T., & Nurowski, P. (2010). Ambient metrics for n-dimensional pp-waves. Communications in Mathematical Physics, 296(3), 881-898.
DOI Scopus27 WoS28
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 Scopus58 WoS53
2007 Leistner, T. (2007). On the classification of Lorentzian holonomy groups. Journal of Differential Geometry, 76(3), 423-484.
DOI Scopus66 WoS58
2007 Armstrong, S., & Leistner, T. (2007). Ambient connections realising conformal Tractor holonomy. Monatshefte fur Mathematik, 152(4), 265-282.
DOI Scopus6 WoS7
2006 Leistner, T. (2006). Conformal holonomy of C-spaces, Ricci-flat, and Lorentzian manifolds. Differential Geometry and its Applications, 24(5), 458-478.
DOI Scopus44 WoS47
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 Scopus27 WoS32

Year Citation
2020 Dearricott, O., Tuschmann, W., Nikolayevsky, Y., Leistner, T., & Crowley, D. (Eds.) (2020). Differential Geometry in the Large (Vol. 463). Cambridge University Press.
DOI Scopus1
2020 Dearricott, O., Tuschmann, W., Nikolayevsky, Y., Leistner, T., & Crowley, D. (Eds.) (2020). Differential Geometry in the Large (Vol. 463). Cambridge University Press.
DOI Scopus1
2004 Leistner, T. (2004). Holonomy and Parallel Spinors in Lorentzian Geometry. Berlin: Logos Verlag.

Year Citation
2021 Fresacher, M. (2021). Approximation of Higher Degree Spectra Results for Twisted Laplace Operators.

Year Citation
2024 Greenwood, S., & Leistner, T. (2024). Lorentzian homogeneous structures with indecomposable holonomy.
2024 Gover, A. R., Kress, J., & Leistner, T. (2024). Conformal Killing tensors and their Killing scales.
2023 Cortés, V., & Leistner, T. (2023). Compact Locally Conformally Pseudo-Kähler Manifolds with Essential
Conformal Transformations.
2023 Costanza, F., Eastwood, M., Leistner, T., & McMillan, B. (2023). The range of a connection and a Calabi operator for Lorentzian locally
symmetric spaces.
2023 Alekseevsky, D., Cortes, V., & Leistner, T. (2023). Geometry and holonomy of indecomposable cones.
DOI
2022 Leistner, T., & Teisseire, S. (2022). Conformal transformations of Cahen-Wallach spaces.
DOI
2021 Fino, A., Leistner, T., & Taghavi-Chabert, A. (2021). Almost Robinson geometries.
DOI
2021 Costanza, F., Eastwood, M., Leistner, T., & McMillan, B. (2021). A Calabi operator for Riemannian locally symmetric spaces.
DOI
2021 Leistner, T., & Teisseire, S. (2021). Fundamental regions for non-isometric group actions.
DOI
2020 Fino, A., Leistner, T., & Taghavi-Chabert, A. (2020). Optical geometries.
DOI
2016 Anderson, I. M., Leistner, T., Lischewski, A., & Nurowski, P. (2016). Conformal Walker metrics and linear Fefferman-Graham equations.
DOI
2007 Leistner, T. (2007). Towards a classification of Lorentzian holonomy groups. Part II: Semisimple, non-simple weak-Berger algebras.
DOI

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 IM

Mathematics IA

Mathematics IB

Applications of Quantitative Methods in Finance I

Multivariable and Complex Calculus II

Groups and Rings III

Topology and Analysis III

Advanced Mathematical Perspectives III

Manifolds, Lie Groups and Lie Algebras (Honours)

Differential Geometry (Honours)

 

 

Date Role Research Topic Program Degree Type Student Load Student Name
2025 Principal Supervisor Conformal transformations of Lorentzian manifolds Master of Philosophy Master Full Time Mr Dylan Nicholas Holland
2025 Co-Supervisor Kupka-Smale theorem in elliptic complex geometry Master of Philosophy Master Part Time Miss Lee Ward
2025 Co-Supervisor K-Theory of Topological Insulators Doctor of Philosophy Doctorate Full Time Mr Joshua Celeste
2024 Co-Supervisor Cohomology Rings of Topological and Smooth 4-Manifolds Master of Philosophy Master Full Time Mr Paawan Nileshkumar Jethva
2024 Principal Supervisor Conformally related Einstein metrics Master of Philosophy Master Full Time Mr Harrison Greven

Date Role Research Topic Program Degree Type Student Load Student Name
2022 - 2024 Principal Supervisor Algebraic Aspects of Lorentzian Homogeneous Spaces Master of Philosophy Master Full Time Mr Steven James Greenwood
2022 - 2024 Co-Supervisor Quadrics & Quadrals, Combinatorics & Characterisations: a Survey of Subspaces Master of Philosophy Master Full Time Mr George Savvoudis
2020 - 2023 Principal Supervisor On Dirac Generating Operators and Clifford Module Bundles Doctor of Philosophy under a Jointly-awarded Degree Agreement with Doctorate Full Time Ms Manasa Manjunatha
2020 - 2025 Co-Supervisor The Oka Principle in Higher Twisted K-Theory Doctor of Philosophy under a Jointly-awarded Degree Agreement with Doctorate Full Time Miss Haripriya Sridharan
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 Principal Supervisor Symmetric Spaces, Geometric Manifolds and Geodesic Completeness Master of Philosophy Master Full Time Mr Thomas Jack Munn
2019 - 2023 Principal Supervisor The Killing operator on locally homogeneous spaces Doctor of Philosophy Doctorate Full Time Mr Esteban Federico Costanza
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

Date Role Membership Country
2010 - ongoing Member Australian Mathematical Society Australia

Date Title Engagement Type Institution Country
2022 - ongoing Differential Geometry Seminar Scientific Community Engagement University of Adelaide Australia
2021 - 2021 Event Director of the AMSI Summer School in the Mathematical Sciences Scientific Community Engagement Australian Mathematical Sciences Institute and University of Adelaide Australia
2018 - 2018 Conference Director of the 62nd Annual Meeting of the Australian Mathematical Society Scientific Community Engagement University of Adelaide Australia

Date Role Editorial Board Name Institution Country
2016 - 2019 Board Member Communications of the Korean Mathematical Society Korean mathematical Society Korea, Republic of
2014 - ongoing Board Member Advances in Geometry De Gruyter Germany

Date Topic Presented at Institution Country
2024 - 2024 Lorentzian homogeneous structures with indecomposable holonomy Symmetry and shape University of Santiago de Compostela Spain
2024 - 2024 Lorentzian homogeneous structures with indecomposable holonomy Seminar on Differential Geometry University of Hamburg Germany
2024 - 2024 Lorentzian homogeneous structures with indecomposable holonomy Differential geometry seminar University Regensburg Germany
2024 - 2024 The Killing connection and the range of the Killing operator Mathematical supergravity Universidad Nacional de Educación a Distancia, UNED, Madrid Spain
2023 - 2023 Conformal transformations of Cahen-Wallach spaces Research Seminar Differential Geometry University of Hamburg Germany
2023 - 2023 The Killing connection and the range of the Killing operator Differential Geometry Seminar University Regensburg Germany
2023 - 2023 Conformal transformations of Cahen-Wallach spaces Spectrum and Symmetry for Group Actions in Differential Geometry II Matrix Mathematical Research Institute Australia
2023 - 2023 The range of a connection and a Calabi operator for Lorentzian locally symmetric spaces GRIEG meets Chopin. Warsaw meeting on geometric methods in science Polish Academy of Science Poland
2022 - 2022 Conformal Transformation of Cahen-Wallach spaces Oberseminar University of Regensburg Germany
2022 - 2022 A Calabi operator for locally symmetric spaces Global Analysis on Manifolds A Conference in Honour of Prof. Christian Bär University Freiburg Germany
2022 - 2022 Conformal Transformations of Cahen-Wallach spaces Pseudo-Riemannian geometry and invariants in General Relativity University of Stavanger Norway
2021 - 2021 Cauchy problems for Lorentzian manifolds with special holonomy. Part 1 Seminar on Advanced Topics in Geometric Analysis University of Regensburg Germany
2021 - 2021 Geodesic completeness of compact Lorentzian manifolds International Meeting on Lorentzian Geometry University of Cordoba Spain
2019 - 2019 Semi-Riemannian cones and their holonomy THE ABEL SYMPOSIUM 2019: Geometry, Lie Theory and Applications Norwegian Academy of Science and Letters Norway
2019 - 2019 The ambient obstruction tensor and conformal holonomy Workshop on Cartan Geometry Korea Institute for Advanced Study Korea, Republic of
2018 - 2018 The ambient obstruction tensor and conformal holonomy Conformal and Symplectic Geometry University of Auckland New Zealand
2017 - 2017 Geodesic completeness of compact Lorentzian manifolds Seminario de Geometría University of Granada Spain
2017 - 2017 Lecture series on non Riemannian holonomy Simons Semester Symmetry and Geometric Structures Institute of Mathematics of the Polish Academy of Science Poland
2016 - 2016 Cauchy problems for Lorentzian manifolds with special holonomy Geometric Flows and the Geometry of Space-time University of Hamburg Germany
2016 - 2016 Geodesic completness of compact Lorentzian manifolds with spacial holonomy 7th Pacific RIM Conference on Mathematics Seoul National University Korea, Republic of
2016 - 2016 Cauchy problems for Lorentzian manifolds with special holonomy Workshop on Analysis, Geometry and Mathematical Relativity Monash University Australia

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