About me

I am a mathematician/mathematical physicist and a researcher in mathematics education in the Analysis, Geometric Structures and Mathematical Physics section of the Faculty of Mathematics at the University of Vienna. I am the coordinator of the Austrian Science Fund's (FWF) Emerging Fields project:

A new geometry for Einstein's Theory of Relativity and Beyond



My research interests include:


    mathematical physics/mathematical general relativity:

  • spacetime singularities, cosmic censorship, exact radiative spacetimes, impulsivge gravitational waves

    • mathematics education:

  • professional knowledge of teachers, beliefs on teaching and learning mathematics

    • (applied) mathematics:

  • generalized functions, theory of PDE, kinetic theory, time frequency analysis & modulation spaces


What i'm doing


  • Book


    I have co-authored the general introductory book Einführung in das Mathematische Arbeiten (German, Introduction into mathematical methodology) with Hermann Schichl. Together we are running a service web page accompanying the book. We have been awarded the UNIVIE Teaching Award 2013 of Vienna University and the Ars Docendi 2016, the Austrian National Award in University Teaching.

  • Professional Memberships


    Also I am member and treasurer of the IAGF (The International Association for Generalized Functions), a life-time member of ISAAC (The International Society for Analysis, its Applications and Computation), and a member of GDM (The German Society of Didactics of Mathematics).

  • Teaching Portfolio


    My teaching includes a variety of courses in several areas of mathematics reaching from general first-year-courses to specialized courses and seminars in analysis, PDE and geometry, as well as major courses in the teacher’s training programme.

  • Supervisor in MCMP and VSM


    I am a supervisor both in the Vienna Master Class Mathematical Physics (MCMP) which is run jointly by the Faculties of Mathematics and Physics of Vienna University, and Vienna School of Mathematics (VSM) which is a new joint enterprise of the University of Vienna and the Technical University Vienna.

A new geometry for Einstein's Theory of Relativity and Beyond
- The Team

  • Clemes Saemann

    Clemens Saemann

    Clemens Sämann is a Senior Postdoctoral Researcher at the University of Vienna, specializing in Lorentzian geometry, general relativity, and the study of low-regularity spacetimes. His research focuses on synthetic approaches to Lorentzian geometry, including Lorentzian length spaces and causal structure. He has received the START Prize from the Austrian Science Fund and has held positions at top institutions like the University of Oxford and University of Toronto.

  • Raquel Perales

    Raquel Perales

    Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.

  • Michael Kunzinger

    Michael Kunzinger

    Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.

  • Chiara Rigoni

    Chiara Rigoni

    Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.

Daniel lewis

Daniel lewis

1

Pinboard

Everything that has happened

  1. Talks in Turin

    09/2024

    I talked at the GF2024 and gave a invited talk at the Time Machine Factory conference, both in Turin, Italy.

  2. The Hawking theorem in Lipschitz regularity

    19/6/2024

    I gave the invited talk The Hawking theorem in Lipschitz regularity at Queen Mary University of London, U.K.

  3. EPS Conference on Gravitation

    05/2024

    I have been invited as a speaker to the EPS Conference on Gravitation: Unlocking Gravity Through Computation in Prague in December 2024, as well as to the BIRS-IMAG workshop Geometry, Analysis, and Physics in Lorentzian Signature in Granada in May 2025.

  4. The new teaching project MaThX

    04/2024

    The University of Vienna has announced to fund the Faculty's teaching project MaThX (Mathematikunterricht zwischen Theorie und Praxis; Teaching mathematics beteen theory and pratice), where I am a team memeber.

  5. Talk at the Mathematical Society's Teacher Training

    05/04/2024

    Together with Ilse Fischer I gave a talk at the Austrian Mathematical Society's Teacher Training Day entiteled Neue Mathematik für die Schule (New Mtahs for the School).

  6. A new geometry for Einstein's Theory of Relativity and Beyond

    12/03/2024

    The Austrian Science Fund (FWF) has announced to fund the project A new geometry for Einstein's Theory of Relativity and Beyond in its new Emerging Fields excellency propgramme. The funding sum is an unprecedented 7 Mio. Euro. The project team consist of Michael Kunzinger, Raquel Perales, Chiara Rigoni, Clemens Sämann, and myself. See the press releases of FWF, the University of Vienna and the Faculty of Mathematics.

  7. Invited Lecture at the Mathematical Society's Teacher's Day

    22/09/2023

    Together with Ilse Fischer I gave an invited lecture at the Teacher's Day of the Austrian Mathematical Society.

  8. Clemens Sämann gets awarded START-prize of the Austrian Science fund

    06/2023

    Clemens Sämann, graduate from our research group and my frequent co-author was arwarded the START-prize of the Austrian Science fund.

  9. invitation the scientific board of GeLoMer

    04/2023

    I was invited to join the scientific board of GeLoMer the XI International Meeting on Lorentzian Geometry, to be held in Merida, Mexico, Jan. 29--Feb. 2, 2024.

  10. Talk at Planetarium

    26/4/2023

    I gave a popular talk on my research at Vienna Planetarium.

  11. conference in Novi Sad

    21/4/2023

    I gave an invited main lecture entiteled Impulsive gravitational waves (From particle motion to geometry) at the HASOP2023 conference in Novi Sad, Serbia.

  12. Our workshop about Non-regular Spacetime Geometry gets hosted mby the ESI

    13-24/03/2023

    The ESI hosted our workshop Non-regular Spacetime Geometry, co-organised with Piotr Chrusciel, Melanie Graf, Ettore Minguzzi, and Mike Kunzinger.

  13. something about General Relativity and Gravitation

    16/02/2023

    The Topical Collection "Singularity theorems, causality, and all that (SCRI21)", which I was co-editing appeared topday in General Relativity and Gravitation.

  14. Research Milestones and Academic Achievements in 2022: Conferences, Ph.D. Successes, and Invited Talks

    2022

    The International Conference on Generalized Functions GF2022 organzied by our research group took place at our Faculty in Vienna. My student Benedict Schinnerl defended his Ph.D. thesis with best marks. My Ph.D. student Argam Ohanyan received a DOC-grant from the Austrian Academy of Science. He also successfully defended his master thesis in Pysics. I gave the invited main talk Raumzeitsingularitäten: Die Theoreme von Penrose und Hawking (Spacetime singularities: The theorems of Penrose and Hawking) at the ÖMG-Fortbildungstagung für Lehrhräfte (Meeting for continuing education of teachers of the Austrian Mathematical Society).

  15. Solidarity with Ukraine

    25/2/2022

    Solidarity with Ukraine

  16. Collaborative Projects, Workshops, and Research Highlights: Funding Success and Academic Contributions

    2021

    The project application Marginally outer trapped tubes of Walter Simon, where I am a co-applicant was selected for funding by FWF. I was co-organizing the small 2021 Null Distance Workshop with Cristina Sormani. The talks and slides of the online-meeting SCRI21: Singularity theorems, causality, and all that (A tribute to Roger Penrose) which was held June 14-18, 2021, and which I was co-organizing are now available from the conference website under https://sites.google.com/unifi.it/scri21/program. The talks of the 10th International Meeting on Lorentzian Geometry GeLoCor, where I was a member of the scientific commitee are now available on a Youtube channel. My FWF-funded research project Non-smooth spacetime geometry has started with two Ph.D. students employed, Matteo Calisti and Felix Rott.

  17. Funding Success and Scholarship Award for Ph.D. Student

    2020

    My project application Non-smooth spacetime geometry was selected for funding by FWF. My Ph.D. student Benedict Schinnerl was awarded a Uni:Docs scholarship.

  18. public lecture at Planetarum

    2019

    I gave a public lecture at Planetarium Wien about Raumzeitsingularitäten.

  19. Jiri Podolsky has written a background story on his research for CQG+

    2019

    Jiri Podolsky, a theoretical physicist from Charles University at Prague (and a frequent collaborator of mine) has written a background story on his research for CQG+. It is entiteled Understanding exact space-times and also briefly describes our joint project(s).

  20. Book in collaboration with Hermann Schichl

    2018

    The 3rd edition of the textbook Einführung in das mathematische Arbeiten (German; Introduction into mathematical methodology) with Hermann Schichl has just appeared. For the product flyer click here. The service page of the book http://www.mat.univie.ac.at/~einfbuch has been updated. Also the series of explanatory videos which we have produced acompanying the 3rd edition is available freely from there.

Research

Research Interests

I was originally trained as a mathematical physicist specializing in general relativity. Over the years I have developped a broad interest in several topics in analysis, geometry and mathematical physics, as well as in mathematics education. My current research interests include but are not confined to the following list:


    Mathematical General Relativity

  • semi-Riemannian geometry in low regularity
  • singularity theorems and cosmic censorship
  • exact solutions: impulsive gravitational waves

    • Algebras of Generalized Functions and Applications

  • geometric theory of nonlinear generalized functions
  • applications in general relativity
  • applications in PDE, in particular regularity theory
  • structure theory of algebras of generalized functions

    • Mathematics education

  • professional knowledge of teachers
  • beliefs on teaching and learning mathematics
  • didactic of analysis

    • Nonlinear PDE/Kinetic theory


    Time frequency analysis/Modulation spaces


Much of my research was carried out in collaboration with the international research group DiANA (which is an acronym for "Differential Algebras and Nonlinear Analysis") based at the Universities of Vienna and Innsbruck in Austria, the University of Ghent in Belgium, as well as at the University of Southampton and the University of Loughborough in the UK.



For more details on my research you can have a look at

Topics

Mathematical General Relativity

Mathematical General Relativity (GR) is concerned with the mathematical study of Albert Einsteins theory of space, time and gravitation, which was established almost exactly 100 years ago. My own research in this area is mostly concerned with questions of low regularity. In fact, the geometric foundation of GR is Lorentzian geometry which is usually formulated in the smooth category. On the other hand, the nature of GR as a physical theory and its analytic foundations (most notably hyperbolic PDE) demand the use of non-smooth functions and regularity issues become essential.

  • One of the foundational tools in Lorentzian and semi-Riemannian geometry is the exponential map, which sends rays in the tangent space to geodesic on the manifold. If the metric is smooth then the exponential map is a local diffeomeorphism and a radial isometry but if the regularity of the metric is below $C^{1,1}$ (i.e., its first derivatives are Lipschitz continuous which guarantees unique local solvability of the geodesic equation) then classical counterexamples show the failure of the ususal convexity properties. These were complimented recently by Chrusciel and Grant who have studied metrics of Hölder class $C^{1,a}$ (a less than 1) where the lightcones `bubble up' (i.e. fail to be hypersurfaces).
    A positive result was achieved in [P34] together with Michael Kunzinger and his Ph.D student Milena Stojkovic, where we have shown that if the metric is $C^{1,1}$ then the exponential map retains the maximal regularity, i.e., it is a bi-Lipschitz homeomorphism. Based in these results and techniques (a careful regularisation approach combined with techniques from comparison geometry), and with James Vickers joining the team, we could show in [P35] that the bulk of the ususal smooth Lorentzian causality theory remains valid also in the regularity class $C^{1,1}$. This in turn enabled us to provide the first proof of a $C^{1,1}$-singularity theoreom, namely the Hawking one in [P38]. Furthermore we could also establish the Penrose singularity theorem in regularity $C^{1,1}$ in [P40]. Current research in this direction is concerned with the proof of the most general singularity theorem, namely the Hawking-Penrose one in this regularity class, and the use of techniques of comparison geometry to further lower the regularity assumptions in the singularity theorems.


  • Also since a long time I have been involved in the study of impulisve gravitational waves. These are exact spacetimes which model short but intense bursts of gravitational radiation. From a mathematical viewpoint, they are key examples of spactimes of low regularity, which are either described by a distributional metric or a metric of Lipschitz regularity. I have primarily been concerned with the study of geodesics in these geometries and with questions of completeness. Starting from my Ph.D days I have in part together with Michael Kunzinger studied the simplest model, i.e., impulsive pp-waves using nonlinear distributional geometry, see [P1-P6]. Also long ago, joining with Jiri Podolsky from Charles University in Prague I have studied expanding impulsive gravitational waves in Minkowski background ([P14]). This cooperation has been stalled for a some time but was revived some 5 yeas ago when Jiri's Ph.D. student Robert Svarc took up this topic. Together we have studied gyratons, i.e., impulsive gravitational waves with spin in [P36], a study which nicely complements work I had done previoiusly together with Clemens Sämann on impulsive waves with a general wave surface ([P30,P39]). The oberservation that Filippov's solutions concept is very well-suited to describe geodesics in Lipschitz space times ([P33]) boosted our cooperation and made it possible to provide a mathematical study of completeness of non-expanding impulsive waves on all constant curvature backgrounds ([P32,37]). Current work is concerned with the study of completeness in expanding impulsive waves on all constant curvature backgrounds and with an investigation of the 'general Brinkmann metric' which combines the effects of a general wave surface with that of a spin.


  • The study of geodesics in impulsive pp-waves using nonlinear distributional geometry based on algebras of generalized functions has triggered a research line in generalized functions which lead to the development of a theory suitable to be applied in a geometric setting. This has been applied to deal with the (distributional-)Schwarzschild geometry ([P10]), and more generally the topic of linear and nonlinear distributional general relativity has been reviewed in [P15] and more recently in [P21] (jointly with James Vickers). In particular, we have related the nonlinear framework to the `maximal reasonable' class of distributional metrics of Geroch and Traschen in [P26], see aslo [P23]. An up-to-date review on this topic has been provided by Eduard Nigsch and Clemens Sämann.



Algebras of generalized functions and applications

Algebras of generalized functions, also known as Colombeau Algebras, are sheaves of differential algebras which contain the vector space of Schwartz distributions as a subspace and the space of smooth functions as a subalgebra, hence provide a framework for multiplying distributions which benefits from maximal compatibility with classical analysis (read more...) In particular, I'm interested in all geometric aspects of this theory and its applications, most of all in general relativity and PDE.

  • Michael Kunzinger and myself, partly in collaboration with James Vickers and Michael Oberguggenberger have developped the foundations of global analysis as well as (semi-)Riemannian geometry with generalized functions in Colombeau's so-called special setting ([P9, P11, P12, P17, P18, J24]), which we called non-linear distributional geometry. Some classical questions which we had encountered when dealing with flows of singular vector fields have been solved in collaboration with Hermann Schichl ([P20]).

  • Together with Michael Grosser and again Michael Kunzinger and James Vickers I have developped a diffeomorphism invariant full Colombeau algebra on differentiable manifolds ([P8])---a task which needed restructuring some of the foundations of the theory in Euclidean space and which has been achieved in collaboration with Eva Farkas ([M1]). The idea of this research is explained in [P7] while an overview is presented in [P16]. Finally in [P27] I have reported on a significant shift of focus which is indispensable when dealing with the tensor case (see below). Significant earlier parts of this research have been collected in the monograph [M2] with Michael Grosser, Michael Kunzinger and Michael Oberguggenberger.
    One big challenge in the theory of diffeomorphism invariant full Colombeau algebras has been to construct spaces of generalized tensor fields. By the Schwartz impossibility result the obvious approach of taking the tensor product of the full algebra on a manifold with classical tensor fields is ruled out and one has to take a different route. By introducing a suitable class of transport operators (an idea put forward by James Vickers long time ago) and letting generalized fields depend on them Michael Grosser, Michael Kunzinger, James Vickers and myself could finally construct such spaces in [P28]. This line of research has been further developped by Eduard Nigsch, in part together with James Vickers and Michael Grosser.


  • As an application in PDE I have, together with Eberhard Mayerhofer and James Grant studied local solvability of the wave equation on weakly singluar space-times ([P25]). This result has been extended to a global one together with Günther Hörmann and Michael Kunzinger in ([P29] and relations to first oder systems have been investigated in [P31] in collaboration with my Ph.D. student Clemens Hanel and Güther's Ph.D. student Christian Spreitzer.


Kinetic theory

I have also done some work in nonlinear PDE, more precisely in collissionless models in kinetic theory. Together with Gerhard Rein, Michael Kunzinger and Gerald Teschl I have studied the Vlasov-Klein-Gordon system: In [P13] we have proven the existence of local weak solutions, while in [P19] we have derived local classical solvability plus a continuation criterion. Again with Michael Kunzinger and Irina Kmit I have studied singular solutions of the Vlaosov-Poisson system ([P22]) with the aim of looking at the singular limits of the VP-system, i.e., the Euler equations and the n-body problem.

Gravitational waves

Quite early in my career I developped some interest in gravitational wave detection, which resulted in two fun-papers [Mi1] and [Mi3] where together with some fellow students as well as Karsten Danzmann we put forward the idea of a space-borne gravitational wave detector much larger than LISA. Of course such a project is not at all feasable.

Publications

Research Monographs

[M2] Geometric Theory of Generalized Functions (with Applications to General Relativity)
(This item received a Featured Review by the AMS)
Authors: Michael Grosser, Michael Kunzinger, Michael Oberguggenberger, Roland Steinbauer
MSC-class: 46F30; 35A30, 35Q75, 46-02, 46T30, 58-02, 83C99
Ref: Mathematics and its Applications, Vol. 537, Kluwer, Dodrecht, 2001.

[M1] On the foundations of nonlinear generalized functions I,II
(This item received a Featured Review by the AMS)
Authors: Eva Farkas, Michael Grosser, Michael Kunzinger, Roland Steinbauer
MSC-class: 46F30, 26E15, 46E50, 35D05
Ref: Mem. Amer. Math. Soc. 729, 153, 2001.
ArXiv: math.FA/9912214

Textbook

[T1] Einführung in das mathematische Arbeiten
(German; Introduction to working mathematically.)
Authors: Hermann Schichl, Roland Steinbauer
MSC-Class: 00A35; 00A05, 00-01
Springer Spektrum, Berlin
1st edition, 2009.
2nd, revised Edition, 2012.
3rd, revised Edition, with additional video-material, 2018.



Preprints

[Pre3] Nulls shells with pressure in Minkowski space
Authors: Miguel Manzano, Marc Mars, Argam Ohanyan, Roland Steinbauer
Status: in preparation

[Pre2] Conjugate points in Lorentzian length spaces
Authors: Michael Kunzinger, Argam Ohanyan, Benedict Schinnerl, Roland Steinbauer
MSC-class: 52C23, 53C50, 53B30, 51K10, 53C80
Status: in preparation.

[Pre1] Marginally outer trapped tubes in de Sitter spacetime
Authors: Marc Mars, Carl Rossdeutscher, Walter Simon, Roland Steinbauer
ArXiv: arXiv:2407.10602 [gr-qc]
Status: to appear in LMP.

Peer-reviewed Research Articles

[P57] Cut-and-paste for impulsive gravitational waves with $\Lambda$: The mathematical analysis
Authors: Clemens Sämann, Benedict Schinnerl, Roland Steinbauer, Robert Svarc
MSC-class: 83C15, 83C35, 83C10, 46F10, 34A36
Ref: Lett. Math. Phys. 114, 58, 31pp. (2024)
ArXiv: arXiv:2312.01980[gr-qc]

[P56] The singularity theorems of General Relativity and their low regularity extensions
(Invited review article in Jahresbericht der Deutschen Mathematiker-Vereinigung)
Authors: Roland Steinbauer
MSC-class: 83C75, 53B30, 83-02
Ref: Jahresber. Dtsch. Math.-Ver. 125(2), 73–119 (2023)
ArXiv: arXiv:2206.05939 [math-ph]

[P55] Penrose junction conditions with $\Lambda$: Geometric insights into low-regularity metrics for impulsive gravitational waves
Authors: Jiri Podolsky, Roland Steinbauer
MSC-class: 83C15, 83C35, 83C10
Ref: Gen. Relativ. Gravit. 54, 96 (2022).
ArXiv: arXiv:2205.07254 [gr-qc]

[P54] Null distance and convergence of Lorentzian length spaces
Authors: Michael Kunzinger, Roland Steinbauer
MSC-class: 53C23, 53C50, 53B30, 51K10, 53C80
Ref: Ann. Henri Poincare, 23, 4319--4342 (2022)
ArXiv: arXiv:2106.05393 [math.DG]

[P53] The Hawking-Penrose singularity theorem for $C^1$-Lorentzian metrics.
Authors: Michael Kunzinger, Argam Ohanyan, Benedict Schinnerl, Roland Steinbauer
MSC-class: 83C75, 53B30
Ref: Commun. Math. Phys. 391, 1143--1179 (2022)
ArXiv: arXiv:2110.09176 [math-ph]

[P52] A note on the Gannon-Lee theorem
Authors: Benedict Schinnerl, Roland Steinbauer
MSC-class: 83C75, 53B30
Ref: Lett. Math. Phys. 111(142), 17pp. (2021)
ArXiv: arXiv:2101.04007 [math-ph]

[P51] Causal simplicity and (maximal) null pseudoconvexity
Authors: Jakob Hedicke, Ettore Minguzzi, Benedict Schinnerl, Roland Steinbauer, Stefan Suhr
Ref: Class. Quantum Grav. 38(22), 227002, 13pp. (2021)
ArXiv: arXiv:2105.08998 [gr-qc]

[P50] The future is not always open
Authors: James Grant, Michael Kunzinger, Clemens Sämann, Roland Steinbauer
MSC-class: 83C50, 83C75
Ref: Lett. Math. Phys, 110(1), 83–103, (2020)
ArXiv: arXiv:1901.07996 [math.DG]

[P49] Cut-and-paste for impulsive gravitational waves with $\Lambda$: The geometric picture
Authors: Jiri Podolsky, Clemens Sämann, Roland Steinbauer, Robert Svarc
MSC-class: 83C15, 83C35, 83C10
Ref: Phys. Rev. D 100(2), 024040, 8, (2019)
ArXiv: arXiv:1905.00225 [gr-qc]

[P48] Comment on 'Memory effect for impulsive gravitational waves'
Author: Roland Steinbauer
MSC-class: 82C15, 83C35, 46F10, 34A36
Ref: Class. Quantum Grav. 36(9) 098001, 14, (2019)
ArXiv: arXiv:1811.10940 [gr-qc]

[P47] On geodesics in low regularity
Authors: Clemens Sämann, Roland Steinbauer
MSC-class: 53B30, 53C22, 34A36, 83C99
Ref: Journal of Physics: Conference Series 968, 012010, 14, (2018)
ArXiv: arXiv:1710.10887 [math-ph]

[P46] The Hawking-Penrose singularity theorem for $C^{1,1}$-Lorentzian metrics
Authors: Melanie Graf, James Grant, Michael Kunzinger, Roland Steinbauer
MSC-class: 83C75, 53B30
Ref: Commun. Math. Phys. 360(3), 1009--1042, (2018)
ArXiv: arXiv:1706.08426 [math-ph]

[P45] Geodesics in nonexpanding impulsive gravitational waves with $\Lambda$, part II
(Featured as Editor's pick in Journal of Mathematical Physics)
Authors: Clemens Sämann, Roland Steinbauer
MSC-class: 83C15, 83C35, 46F10, 34A36
Ref: J. Math. Phys. 58(11), 112503, 18, (2017)
ArXiv: arXiv:1704.05383

[P44] Penrose junction conditions extended: impulsive waves with gyratons
Authors: Jiri Podolsky, Robert Svarc, Roland Steinbauer, Clemens Sämann
MSC-class: 83C15, 83C35, 83C10
Ref: Phys. Rev. D 96 064043, 11 (2017)
ArXiv: arXiv:1704.08570

[P43] Completeness of general pp-wave spacetimes and their impulsive limit
Authors: Clemens Sämann, Roland Steinbauer, Robert Svarc
MSC-class: 83C15, 83C35, 83C10, 34A36
Ref: Class. Quantum Grav. 33(21) 215006, 27 (2016)
ArXiv: arXiv:1607.01934

[P42] The global uniqueness and $C^1$-regularity of geodesics in expanding impulsive gravitational waves
Authors: Jiri Podolsky, Clemens Sämann, Roland Steinbauer, Robert Svarc
MSC-class: 83C15, 83C35, 46F10, 34A36
Ref: Class. Quantum Grav. 33(19) 195010, 23 (2016)
ArXiv: arXiv:1602.05020

[P41] Geodesics in nonexpanding impulsive gravitational waves with $\Lambda$, part I
Authors: Clemens Sämann, Roland Steinbauer, Alexander Lecke, Jiri Podolsky
MSC-class: 83C15, 83C35, 46F10, 34A36
Ref: Class. Quantum Grav. 33(11) 115002, 33 (2016)
ArXiv: arXiv:1509.04914

[P40] The Penrose singularity theorem in regularity $C^{1,1}$
(Featured as one of the highligths 2015 in Classical and Quantum Gravity)
Authors: Michael Kunzinger, Roland Steinbauer, James A. Vickers
MSC-class: 83C75, 53B30
Ref: Class. Quantum Grav. 32(15) 155010, 12 (2015)
ArXiv: arXiv:1502.00287

[P39] Geodesic completeness of generalized space-times
Authors: Clemens Sämann, Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35
Ref: in Pseudo-differential operators and generalized functions.
Pilipovic, S., Toft, J. (eds) Operator Theory: Advances and Applications vol. 245. Birkhäuser/Springer, 243--253, 2015.
ArXiv: arXiv:1310.2362

[P38] Hawking's singularity theorem for $C^{1,1}$-metrics
(Featured as one of the highligths 2014/15 in Classical and Quantum Gravity)
Authors: Michael Kunzinger, Roland Steinbauer, Milena Stojkovic, James A. Vickers
MSC-class: 83C75, 53B30
Ref: Class. Quantum Grav. 32(7) 075012, 19 (2015)
ArXiv: arXiv:1411.4689

[P37] The global existence, uniqueness and C^1-regularity of geodesics in nonexpanding impulsive gravitational waves
Authors: Jiri Podolsky, Clemens Sämann, Roland Steinbauer, Robert Svarc
MSC-class: 83C15, 34A36, 83C35
Ref: Class. Quantum Grav. 32 025003, 23 (2015)
ArXiv: arXiv:1409.1782

[P36] Gyratonic pp-waves and their impulsive limit
Authors: Jiri Podolsky, Roland Steinbauer, Robert Svarc
MSC-class: 83C15, 83C35
Ref: Phys. Rev. D 90, 044050, 15 (2014).
ArXiv: arXiv:1406.3227

[P35] A regularisation approach to causality theory for $C^{1,1}$-Lorentzian metrics
Authors: Michael Kunzinger, Roland Steinbauer, James A. Vickers, Milena Stojkovic
MSC-class: 53B30
Ref: Gen. Relativ. Gravit. 46, 1738, 18 (2014).
ArXiv: arXiv:1310.4404

[P34] The exponential map of a $C^{1,1}$-metric
Authors: Michael Kunzinger, Roland Steinbauer, Milena Stojkovic
MSC-class: 53B20, 53B21, 53B30
Ref: Differential Geom. Appl. 34, 14-24 (2014).
ArXiv: arXiv:1306.4776

[P33] Every Lipschitz metric has $C^1$-geodesics
Author: Roland Steinbauer
MSC-class: 53B30, 34A36
Ref: Class. Quantum Grav. 31 057001 (2014).
ArXiv: arXiv:1311.0300

[P32] The regularity of geodesics in impulsive pp-waves
Authors: Alexander Lecke, Roland Steinbauer, Robert Svarc
MSC-class: 83C15, 34A36, 83C35
Status: Gen. Relativ. Gravit. 46 1648 (2014).
ArXiv: arXiv:1310.1322

[P31] Wave equations and symmetric first-order systems in case of low regularity
Authors: Clemens Hanel, Günther Hörmann, Christan Spreitzer, Roland Steinbauer
MSC-class: 46F30; 35L45, 35D30, 35Q75
Ref: in Pseudo-differential operators, generalized functions and asymptotics.
Selected papers of the 8th ISAAC congress, Moscow, Russia, August 22–27, 2011.
Molahajloo, S. et al., (eds) Operator Theory: Advances and Applications vol. 231. Birkhäuser/Springer, 283--296, 2013.
ArXiv: arXiv:1202.0406

[P30] On the completeness of impulsive gravitational wave spacetimes
Authors:Clemens Sämann, Roland Steinbauer
MSC-class: 83C35, 83C75
Ref: Class. Quantum Grav. 29, 245011 (2012).
ArXiv: arXiv:1207.2633

[P29] Wave equations on non-smooth space-times
Authors: Günther Hörmann, Michael Kunzinger, Roland Steinbauer
MSC-class: 46F30; 46T30, 26E15, 58B10, 46A17
Ref: in Asymptotic Properties of Solutions to Hyperbolic Equations, M.~Ruzhansky and J.~Wirth, (eds.)
Progress in Mathematics 301. Birkhäuser, 162--186, (2012).
ArXiv: arXiv:1107.0014

[P28] A global theory of algebras of generalized functions II: tensor distributions
Authors: Michael Grosser, Michael Kunzinger, Roland Steinbauer, James Vickers
MSC-class: 58J45; 35L05, 35L15, 35D99, 46F30
Ref: New York J. Math. 18, 139--199, (2012).
ArXiv: arXiv:0902.1865

[P27] A geometric approach to full Colombeau algebras
Authors: Roland Steinbauer
MSC-class: 46T30; 46F30
Ref: Banach Center Publ. 88, 267--272 (2010).
ArXiv: arXiv:0710.2096

[P26] On the Geroch-Traschen class of metrics
Authors: Roland Steinbauer, James Vickers
MSC-class: 83C75; 46T30, 53B30, 46F10, 46F30
Ref: Class. Quantum Grav. 26, 065001, (2009).
ArXiv: arXiv:0811.1376

[P25] The wave equation on singular space times
Authors: James Grant, Eberhard Mayerhofer, Roland Steinbauer
MSC-class: 83C75; 46F30, 35D05, 35Q75
Ref: Commun. Math. Phys. 285(2), 399--420, (2009).
ArXiv: arXiv:0710.2007

[P24] Sheaves of nonlinear generalized functions and manifold-valued distributions
Authors: Michael Kunzinger, Roland Steinbauer, James Vickers
MSC-class: 46T30; 46F30, 53B20
Ref: Trans. Amer. Math. Soc. 361, 5177-5192, (2009).
ArXiv: math.FA/0609358

[P23] A note on distributional semi-Riemannian geometry
Authors: Roland Steinbauer
MSC-class: 46T30, 53B30, 46F10, 46F30
Ref: Novi Sad J. Math. 38 (3), 189-199 (2008).
ArXiv: arXiv:0812.0173

[P22] Generalized solutions of the Vlasov-Poisson system with singular data
Authors: Irina Kmit, Michael Kunzinger, Roland Steinbauer
MSC-class: 35A05; 46F30, 35Q72, 82C22
Ref: J. Math. Anal. Appl. 340, 575-587, (2008).
ArXiv: math.AP/0601552

[P21] The use of generalized functions and distributions in general relativity
(Featured as one of the highligths 2005/06 in Classical and Quantum Gravity)
Authors: Roland Steinbauer, James Vickers
MSC-class: 8302
Ref: Class. Quantum Grav. 23(10), R91-R114, (2006).
ArXiv: gr-qc/0603078

[P20] Global Gronwall estimates for integral curves on Riemannian manifolds
Authors: Michael Kunzinger, Hermann Schichl, Roland Steinbauer, James Vickers
MSC-class: 53B21, 53C22, 34A26
Ref: Rev. Mat. Complut., 19(1), 133-137, (2006).
ArXiv: math.DG/0412045

[P19] On classical solutions of the relativistic Vlasov-Klein-Gordon system
Authors: Michael Kunzinger, Gerhard Rein, Roland Steinbauer, Gerald Teschl
MSC-class: 35A07; 35Q72; 35Q40; 82C22
Ref: EJDE, Vol. 2005(1), 1-17, (2005).
ArXiv: math.AP/0407028

[P18] Generalised connections and curvature
Authors: Michael Kunzinger, Roland Steinbauer, James Vickers
MSC-class: 53C05, 53B05, 46T30,46F30, 46F20
Ref: Math. Proc. Cambridge Philos. Soc. 139(3), 497--521, (2005).
ArXiv: math.FA/0403040

[P17] Generalized flows and singular ODEs on differentiable manifolds
Authors: Michael Kunzinger, Michael Oberguggenberger, Roland Steinbauer, James Vickers
MSC-class: 46F30, 34G20, 46T30, 53B20
Ref: Acta Appl. Math, 80, 221-241, (2004).
ArXiv: math.FA/0304131

[P16] Diffeomorphism invariant Colombeau algebras. Part I: Local theory
Author: Roland Steinbauer
MSC-class: 46F30, 46E50, 35D05, 26E15
Ref: Nonlinear Algebraic Analysis and Applications, Proceedings of the International Conference on Generalized Functions (ICGF 2000),
edited by A. Delcroix, M. Hasler, J.-A. Marti and V. Valmorin, Cottenham, Cambridge, Cambridge Scientific Publishers 2004, 333-344 (2004).
ArXiv: math.FA/0104269

[P15] Nonlinear distributional geometry and general relativity
Authors: Roland Steinbauer
MSC-class: 46F30, 46T30, 46F10, 83C05, 83C35
Ref: Nonlinear Algebraic Analysis and Applications, Proceedings of the International Conference on Generalized Functions (ICGF 2000),
edited by A. Delcroix, M. Hasler, J.-A. Marti and V. Valmorin, Cottenham, Cambridge, Cambridge Scientific Publishers 2004, 345-356 (2004).
ArXiv: math-ph/0104041

[P14] Geodesics in spacetimes with expanding impulsive gravitational waves
Authors: Jiri Podolsky, Roland Steinbauer
MSC-class: 83C15, 83C35
PACS-class: 04.20.Jb, 04.30.Nk
Ref: Phys. Rev. D, 67, 0604013, (2003).
ArXiv: gr-qc/0210007

[P13] Global weak solutions of the relativistic Vlasov-Klein-Gordon system
Authors: Michael Kunzinger, Gerhard Rein, Roland Steinbauer, Gerald Teschl
MSC-class: 35D05, 35Q72, 35Q40, 82C22
Ref: Commun. Math. Phys., 238, 367-378 (2003).
ArXiv: math.AP/0209303

[P12] Intrinsic characterization of manifold-valued generalized functions
Authors: Michael Kunzinger, Roland Steinbauer, James Vickers
MSC-class: 46T30, 46F30, 53B20
Ref: Proc. London Math. Soc., 87(2), 451-470 (2003).
ArXiv: math.FA/0107057

[P11] Generalized pseudo-Riemannian geometry
Authors: Michael Kunzinger, Roland Steinbauer
MSC-class: 46F30, 46T30, 46F10, 83C05
Ref: Trans. Amer. Math. Soc. 354(10), 4179-4199 (2002).
ArXiv: math.FA/0107057

[P10] Remarks on the distributional Schwarzschild geometry
Authors: Mark J. Heinzle, Roland Steinbauer
MSC-class: 83C15, 83C15, 83C75, 46F30
Ref: J. Math. Phys. 43(3), 1493-1508 (2002).
ArXiv: gr-qc/0112047

[P9] Foundations of a nonlinear distributional geometry
Authors: Michael Kunzinger, Roland Steinbauer
MSC-class: 46F30, 46T30, 46F10, 37J05
Ref: Acta Appl. Math. 71, 179-206, (2002).
ArXiv: math.FA/0102019

[P8] A global theory of algebras of generalized functions
Authors: Michael Grosser, Michael Kunzinger, Roland Steinbauer, James Vickers
MSC-class: 46F30, 46T30
Ref: Adv. Math., 166, 50-72 (2002).
ArXiv: math.FA/9912216

[P7] Diffeomorphism invariant construction of nonlinear generalized functions
Authors: Michael Grosser, Michael Kunzinger, Roland Steinbauer, Helmuth Urbantke, James Vickers
MSC-class: 46F30, 46T30
Ref: Proceedings of Journees Relativistes 99, Annalen der Physik, Vol 9, Spec. Iss., 173-174 (2000).
Download: here

[P6] On the impulsive limit of gravitational waves
Authors: Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35
Ref: Proceedings of the Spanish Relativity Meeting. ERE-99, 307-311 (2000).
Download: here

[P5] Distributional description of impulsive gravitational waves
Authors: Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35, 46F10
Ref: in Nonlinear Theory of Generalized Functions, edited by Michael Grosser, Günther Hörmann, Michael Kunzinger,
Michael Obergugenberger, (CRC Research Notes, 401, Boca Raton, 1999).
Download: here

[P4] A note on the Penrose junction conditions
(Featured as one of the highligths 1999/2000 in Classical and Quantum Gravity)
Authors: Michael Kunzinger, Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35, 46F10
Ref: Class. Quant. Grav, 16, 1255-1264 (1999).
ArXiv: gr-qc/9811007

[P3] A rigorous solution concept for geodesic and geodesic deviation equations in impulsive gravitational waves
Authors: Michael Kunzinger, Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35, 46F10
Ref: J. Math. Phys, 40, 1479-1489 (1999).
ArXiv: gr-qc/9806009

[P2] Geodesics and geodesic deviation for impulsive gravitational waves
Authors: Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35, 46F10
Ref: J. Math. Phys. 39, 2201-2212 (1998).
ArXiv: gr-qc/9710119

[P1] The ultrarelativistic Reissner-Nordstrom field in the Colombeau algebra
Authors: Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35, 46F10
Ref: J. Math. Phys. 38, 1614-1622 (1997).
ArXiv: gr-qc/9606059

Miscellaneous

[Mi4] Ultrarelativistic Black Holes
Author: Roland Steinbauer
Ref: Contribution to the art book YOUBLACKHOLE (Revolver Publishing, Berlin, 2014) by Tomas Eller
Download: here

[Mi3] Large space interferometer for cosmology
Authors: Karsten Danzmann S. Husa, A. Nairz, B. Pocza, R. Steinbauer
MSC-class: 83C35, 83-05, 83F05
Ref: Proposal to the European Space Agency for a Flexi Mission in Fundamental Physics, (2000).
Download: here

[Mi2] On the geometry of impulsive gravitational waves
Authors: Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35, 46F10
Ref: Prepared for "Proceedings of the 8-th National Romaninan Conference on GRG, Bistritza, June 1998",
which to my best konwledge never appeared
ArXiv: gr-qc/9809054

[Mi1] ELFI, A Gravitational Wave Detector for Cosmology
Authors: S. Husa, A. Nairz, B. Pocza, R. Steinbauer
MSC-class: 83C35, 83-05, 83F05
Ref: Fundamental Physics in Space, Proceedings of the Alpbach Summer School 1997, edited by A. Wilson, 45-47 (ESA Publications Division, Noordwijk, 1997).
Download: here

Mathematics Education Research

[D14] Grundvorstellungen zum Konzept der Differenzierbarkeit von angehenden Mathematiklehrer*innen
(German: Basic mental images on differentiability of preservice teachers)
Authors: Stefan Götz, Antonia Spannagl, Roland Steinbauer
Ref: Mathematikdidaktische Impulse aus Vergangenheit und Gegenwart. Ambrus, G., Sjuts, J., Vásárhelyi, É. (Hrsg.). Münster: WTM-Verlag, S. 51--66 (2024).

[D13] Perceptions of continuity of pre-service teachers in Austria
Authors: Stefan Götz, Antonia Spannagl, Roland Steinbauer
Ref: In P. Drijvers et al. (Eds.), Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13), pp. 3403--10 (2023).

[D12] Conceptions of student teachers on the limit concept
Authors: Christoph Ableitinger, Stefan Götz, Roland Steinbauer
Ref: In P. Drijvers et al. (Eds.), Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13), pp. 3329--36 (2023).

[D11] Raumzeitsingularitäten - Die Theoreme von Penrose und Hawking
(German: Spacetime singularities. The theorems of Penrose and Hawking)
Author: Roland Steinbauer
Ref: Schriftenreihe zur Didaktik der Mathematik der Österreichischen Mathematischen Gesellschaft, Heft 55, 85--105 (2022).

[D10] Vorstellungen von Lehramtsstudierenden zum Grenzwertbegriff
(German: Perceptions of B.Ed. students of the notion of the limit)
Authors: Christoph Ableitinger, Stefan Götz, Roland Steinbauer
Ref: Mathematica Didactica 45, 21pp. (2022).

[D9] Die Entzauberung des Unendlichen (German: The demystification of inifinity)
Author: Roland Steinbauer
Ref: Schriftenreihe zur Didaktik der Mathematik der Österreichischen Mathematischen Gesellschaft, Heft 53, 135--150 (2021).

[D8] Vorstellungen von Lehramtsstudierenden zum Grenzwertbegriff
Authors: Christoph Ableitinger, Roland Steinbauer
Ref: In Hans-Stefan Siller, Wolfgang Weigel, Jan Franz Wörler (Hrsg.), Beiträge zum Mathematikunterricht 2020 (S. 905–908). Münster: WTM-Verlag.
download pdf

[D7] Adressatenspezifische Gestaltung von Fachvorlesungen im Lehramt: eine Fallstudie als Anstoß für vertiefte Reflexionen
(German; Specific design of mathematics courses in the teacher training progamme: a case study)
Authors: Christoph Ableitinger, Harald Kittinger, Roland Steinbauer
Ref: Mathematica Didactica 43(2), 77--94, (2020).

[D6] Beiträge der fachlichen Ausbildung zur Bewältigung von Anforderungen der Unterrichtspraxis
(German; Contributions of subject matter training to mastering classroom practice)
Authors: Christoph Ableitinger, Roland Steinbauer
Ref: in Bedarfsgerechte fachmathematische Lehramtsausbildung. Zielsetzungen und Konzepte unter heterogenen Voraussetzungen Springer, Berlin, (2020)
download preprint[pdf]

[D5] Bedarfsorientierte Gestaltung von Fachvorlesungen für Lehramtsstudierende
(German; Demand-based design of mathematics lecture-courses in the teachers' curriculum)
Authors: Christoph Ableitinger, Roland Steinbauer
Ref: in Beiträge zum Mathematikunterricht, WTM-Verlag Stein, Münster, 2017.

[D4] Einführung in das mathematische Arbeiten – der Passage-Point an der Universität Wien
(German; Introduction into mathematical methodology: the passage point at Vienna University)
Authors:Roland Steinbauer, Evelyn Süss-Stepancik, Hermann Schichl
Ref: in Mathematische Vor- und Brückenkurse edited by Bausch, I et al. Springer Spektrum, 2014, 410--424.
Preprint: pdf

[D3] Grenzwert -- quo vadis?
Ein Pilotprojekt zur Analysis-Ausbildung von Lehramtsstudierenden im Unterrichtsfach Mathematik
(German; Limits -- quo vadis? A pilot project in the analysis education in the teacher's curriculum at the University of Vienna)
Authors: Stefan Götz, Roland Steinbauer
Ref: Einreichung zum Lehrpreis Ars docendi 2013 - Staatspreis für exzellente Lehre an den öffentlichen Universitäten Österreichs (Innovative Lehrkonzepte)
Download: pdf

[D2] Einführung in das mathematische Arbeiten: Ein Projekt zur Gestaltung der Studieneingangsphase an der Universität Wien
(German; Introduction into scientific work in mathematics.)
Authors: Hermann Schichl, Roland Steinbauer
Ref: Mitteilungen der DMV (Notices of the German Mathematical Society), 17(4), 244--246, (2009).
Download: pdf

[D1] Fachdidaktik und Fachwissenschaft Mathematik - zwei Seiten einer Medaille? Mathematik als Forschungsgebiet unter didaktischen Gesichtspunkten - ein essenzieller Bestandteil der Lehramtsausbildung
(German; Mathematics subject didactics and scientific discipline - two sides of the same coin?)
Authors: Stefan Götz, Hans-Christian Reichel, mit Beiträgen von C. Baxa, R. Bürger, M. Fulmek, M. Grosser, M. Hoffmann-Ostenhof, G. Hörmann, A. Kriegl, M. Kunzinger, P. Raith, R. Steinbauer und G. Teschl
Ref: in Alois Ecker (Hrsg.) "Fachdidaktik im Aufbruch. Zur Situation der Lehramtsstudien an der Universität Wien" (Peter Lang Europäischer Verlag der Wissenschaften, Frankfurt am Main) S. 266--286 (2005).

Theses

[H] Nonlinear Distributional Geometry
Authors: Roland Steinbauer
MSC-class: 46F30, 83C35, 83C15, 46F10, 46F05, 83C75
Ref: Habilitationsschrift at the University of Vienna, 2002.
Download: here

[Ph.D.] Distributional Methods in General Relativity
Authors: Roland Steinbauer
MSC-class: 46F30, 83C35, 83C15, 46F10, 46F05, 83C75
Ref: Ph.D. thesis at the University of Vienna, 2000.
Download: here

[M.Sc.] Colombeau Theorie und ultrarelativistischer Limes
Authors: R. Steinbauer
MSC-class: 46F30, 83C35, 83C15, 46F10, 46F05, 83C75
PACS-class: 04.20.Cv, 02.30.Sa, 04.20.Jb, 04.30.-w
Ref: Master's thesis at the University of Vienna, 1995.
Download: here

Editorial Activities

[E2] Singularity theorems, causality, and all that (SCRI21)
Special Issue of General Relativity and Gravitation
Editors: Piotr T. Chruściel, Greg Galloway, Michael Kunzinger, Ettore Minguzzi, Roland Steinbauer
Ref: Springer, 2023.

[E1] The International Conference on Generalized Functions GF 2009
 Special Issue of Integral Transforms and Special Functions
Editors: Michael Grosser, Michael Kunzinger, Stevan Pilipovic, Roland Steinbauer
Ref: Taylor and Francis, 2011.

Publications listed at arXiv, MathSciNet and ZMAT

You can have a look at my preprints and publications listed at arXiv.org.

If you have permission to do so (i.e., if your home organisation is subscribed) you can also have a look at my publications

Projects

  • This is a list of third-party funded research projects where I have been co-author and co-head.



    • FWF Emerging Fields Project EFP 6-N A new Geometry for Einstein’s Theory of Relativity and Beyond
      Principal Investiagtors: Michael Kunzinger, Raquel Perales, Chiara Rigoni, Clemens Sämann, Roland Steinbauer (Coordinator)
      • 01.10.2024 - 30.09.2029


    • FWF Project PAT1996423 Lorentzian Metric Geometry and Optimal Transport
      • Organizer: Michael Kunzinger
      01.12.2023 - 30.11.2027


    • FWF Project P35078 Marginally outer trapped tubes
      • Organizer: Walter Simon
      01.01.2022 - 31.08.2025


    • FWF Project P33594 Non-smooth spacetime geometry
      • Organizer: Roland Steinbauer
      01.02.2021 - 31.1.2025


    • WTZ Project CZ12/2018 Impulsive Gravitational waves: Mathematicl analysis and physical properties
      • Organizers: Robert Švarc, Clemens Sämann
      01.01.2018 - 31.12.2019


    • FWF Project P28770 Singularity Theorems and Comparison Geometry
      • Organizer: Michael Kunzinger
      01.06.2016 - 31.05.2021


    • WTZ Project CZ15/2013 Mathematical Aspects of Impulsive Gravitational Waves
      • Organizers: Jiří Podolský, Roland Steinbauer
      01.01.2014 - 31.12.2015


    • FWF Project P25326 Nichthtglatte Lorentz-Geometrie und symplektische Geometrie
      • Organizer: Günther Hörmann
      01.02.2013 - 31.01.2018


    • FWF Project P23714 The Geometry of Algebras of Generalized Functions
      • Organizer: Michael Grosser
      16.08.2011 - 15.08.2016


    • FWF Project P20525 Global Analysis in Algebras of Generalized Functions
      • Organizer: Michael Kunzinger
      01.07.2008 - 31.06.2011


    • Doctoral College: Mathematical Analysis and Applications
      • Time-frequency analysis and microlocal analysis
      Members: DIANA Research Group, NuHAG Research Group
      1.10.2006 - 30.9.2009


    • Doctoral College: Differential Geometry and Lie Groups
      • Members: DIANA Research Group, Geometry Research Group
      1.10.2006 - 30.9.2009


    • FWF START Project Y 237: Nonlinear Distributional Geometry
      • Organizer: Michael Kunzinger
      2005 - 2011


    • FWF Project P16742: Geometric Theory of Generalized Functions
      • Organizer: Michael Kunzinger
      1.2.2004 - 1.2.2008


    • FWF Project P12023: Distributional Methods in Einstein's Theory of Gravitation
      • Organizer: Helmuth Urbantke
      01.11.1997 - 31.12.2001


    • OEADW Ph.D. Project DOC-338: Distributional Methods in General Relativity
      • Doctoral Grant of the Austrian Academy of Sciences
      Organizer: Roland Steinbauer
      1996 - 97

    Talks

    2024-09-23: The singularity theorems of General Relativity and their low regularity extensions. (Invited main lecture) TMF2024, Turin, Italy

    2024-09-19: The focusing of geodesics under distributional curvature bounds. GF2024, Turin, Italy

    2024-06-19: The Hawking theorem in Lipschitz regularity. (Blackboard talk, invited) Queen Mary University of London, U.K.

    2024-04-12: Curvature bounds and regularisation. (Invited main lecture) HANDS2024, Novi Sad, Serbia.

    2023-04-21: Impulsive gravitational waves (From particle motion to geometry). HASOP2023, Novi Sad, Serbia.

    2022-06-23: Distributional curvature and the focusing of geodesics. NADu 2022, Dubrovnik, Croatia.

    2019-07-09: Scissors-and-paste with $\Lambda$: The geometric picture. GR22, Valencia, Spain.

    2019-07-08: The future is not always open. GR22, Valencia, Spain.

    2019-05-17: Cut and paste with $\Lambda$. Gravity Lunch Seminar, Insitute for Theoretical Physics, University of Vienna.

    2018-08-29: Impulsive Gravitational Waves and their Mathematics. GF 2018, Novi Sad, Serbia.

    2018-06-20: The classical singularity theorems of GR under optimal regularity conditions. IX International Meeting on Lorentzian Geometry, Warsaw, Poland.

    2017-10-26: Recent results in Lorentzian geometry and GR in low regularity. Applications of Generalized Functions (AGF:HAMSaPDE) Novi Sad, Serbia.

    2017-09-13: The Hawking-Penrose singularity theorem for $C^{1,1}$ Lorentzian metrics. 19th International Congress of the Austrian Mathematical Society Salzburg, Austria.

    2017-06-21: On geodesics in low regularity. Non-regular spacetime geometry. An International Meeting Florence, Italy.

    2016-10-25: The Penrose and Hawking singularity theorems revisited. Insitute for Theoretical Physics, University Prague, Czech Republic.

    2016-09-28: News from low regularity GR. 66. Jahrestagung der Österreichischen Physikalischen Gesellschaft, Vienna.

    2016-09-21: The Singularity Theorems in Low Regularity. 8th International Meeting on Lorentzian Geometry, Malaga, Spain.

    2016-06-15: The Singularity Theorems of General Relativity in Low Regularity. Mathematisches Kolloquium, University of Vienna.

    2014-11-22: News from low regularity GR. Gravity Seminar, Insitute for Theoretical Physics, University of Vienna.

    2014-09-09: Lorentzian Geometry and Low Regularity. GF2014, Southampton, U.K.

    2014-07-05: A Regularisation Approach to Causality Theory for Non-smooth Lorentzian metrics. DANS14, Novi Sad, Serbia.

    2013-09-26: The exponential map of a $C^{1,1}$-metric. 18th OEMG/DMV Congress, Innsbruck, Austria.

    2012-05-25: The wave equation on space-time and low regularity. Gravity Lunch Seminar, Insitute for Theoretical Physics, University of Vienna.

    2011-05-31: The wave equation on space-times of low regularity. Insitute for Theoretical Physics, University Prague, Czech Republic.

    2011-05-29: Linear and nonlinear distributional Lorentzian geometry. Insitute for Theoretical Physics, University Prague, Czech Republic.

    2011-04-18: Wave equations on singular space-times: results and perspectives. GF2011---International Conference on Generalized Functions, Linear and Non-Linear Problems, Université des Antilles et de la Guyane, Martinique, France / F.W.I.

    2010-08-30--2010-09-08: Normally Hyperbolic Operators (lecture notes, slides). Mini-course at the Summer School: Generalised Functions in PDE, Geometry, Stochastics, and Microlocal Analysis, Novi Sad, Serbia.

    2010-06-03: Some contributions of Stevan Pilipovic to the structural theory of Colombeau algebras. GFSE10 Generalized Functions---Special Edition, Novi Sad, Serbia.

    2009-09-22: On Lorentzian metrics of low differentiability. 17th International Congress of the Austrian Mathematical Society, Technical University Graz, Austria.

    2009-09-04: On the Geroch-Traschen class of metrics. International Conference on Generalized Functions 2009, University of Vienna, Austria.

    2008-12-03: Semi-Riemannian metrics of low differentiability. International Workshop PDEs and Function Spaces, Imperial College, London, UK.

    2008-09-02: A Note on Distributional Semi-Riemmanian Geometry. 12th Serbian Mathematical Congress, Novi Sad, Serbia.

    2008-02-19: The wave equation on singular space-times (invited). International Symposium Function Spaces and Partial Differential Equations, Osaka, Japan.

    2007-09-03: Towards Tensor-valued Colombeau Functions. Generalized Functions 2007, Stefan Banach Center, Bedlewo, Poland.

    2006-03-09,11: Some topics in kinetic equations I,II (invited). Workshop "Pseudodifferential operators and microlocal analysis", Department of Mathematics and Informatics, Novi Sad, Serbia and Montenegro. .

    2006-01-06: Weak solutions concetps for some kinetic equations (invited). The 1st International Workshop on Mathematical Sciences: Mathematical Analysis and its Applications, Sogang University, Seoul, Korea.

    2004-09-23: Generalized Solutions for a Model in Kinetic Theory. International Conference on Generalized Functions 2004, Topics in PDE, Harmonic Analysis and Mathematical Physics, Novi Sad, Serbia and Motenegro.

    2003-09-25: The relativistic Vlasov-Klein-Gordon system I: Local Classical Solutions. 8th. Meeting of the Austrian Mathematical Society, Bolzano, Italy.

    2003-09-24: Generalized Flows and Singular ODEs on Differentiable Manifolds. 8th. Meeting of the Austrian Mathematical Society, Bolzano, Italy.

    2003-05-15: A Nonlinear Distributional Geometry. Habilitation Colloquium, University of Vienna.

    2003-02-06--15: Winterschool "Nonlinear Partial Differential Equations with Singularities" Main Lecturer, Novi Sad, Yugoslavia.

    2001-09-18: Nonlinear distributional geometry, Part 1. 15th. Congress of the Austrian Mathematical Society.

    2001-09-12: Generalized semi-Riemannian Geometry. Department of Mathematics, University of Southampton, U.K.

    2001-09-06: Generalized pseudo-Riemannian geometry for general relativity. Journees Relativistes 2001, Dublin, Ireland.

    2001-07-16: Geodesics in expanding impulsive gravitational waves. GR16, (16th Conference on General Relativity and Gravitation), Durban, South Africa.

    2001-07-03: Spherical impulsive gravitational waves. Department of Mathematics, University of Southampton, U.K.

    2000-06-14: The geometry of nonlinear generalized functions. Department of Mathematics, University of Innsbruck.

    2000-04-19: Applications of generalized functions in general relativity. International Conference on Generalized Functions 2000, Universite des Antilles et de la Guyane, Guadeloupe, France.

    2000-04-19: Diffeomorphism invariant Colombeau algebras, Part 1: Local theory. International Conference on Generalized Functions 2000, Universite des Antilles et de la Guyane, Guadeloupe, France.

    1999-11-24: Colombeau algebras in general relativity: Impulsive waves and other topics. Institute for Theoretical Physics, Charles University Prague.

    1999-11-23: Colombeau Algebras and Multiplication of Distributions. Institute for Theoretical Physics, Charles University Prague.

    1999-11-03: Algebren verallgemeinerter Funktionen auf Mannigfaltigkeiten. Mathematisches Kolloquium, University of Vienna (joint with M. Grosser).

    1999-09-09: On the impulsive limit of gravitational waves. Spanish Relativity Meeting 1999, University of the Basque Country, Bilbao, Spain.

    1999-06-14: Impulsive Robinson-Trautman Lösungen. Department of Mathematics, University of Innsbruck.

    1999-02-03: "Discontinuous Diffeomorphisms". Department of Mathematics, University of Innsbruck.

    1998-11-14,19,26: Nichtlineare Wellengleichungen. Institute for Theoretical Physics, University of Vienna.

    1998-10-22: Geodäten und Rosen-Form für impulsive Gravitationswellen. Gravity Seminar, Institute for Theoretical Physics, University of Vienna.

    1998-08-31: On the Geometry of Impulsive Gravitational Waves. 2nd Samos Meeting on Cosmology, Geometry and Relativity "Mathematical & Quantum Aspects of Relativity and Cosmology", Pythagoreon, Greece.

    1998-07-14: "Discontinuous Diffeomorphisms". Workshop "Nonlinear Theory of Generalized Functions", Department of Mathematics, Univeristy of Novi Sad, Yugoslavia.

    1998-07-13: Nonlinear Generalized Functions and General Relativity. Workshop "Nonlinear Theory of Generalized Functions", Department of Mathematics, Univeristy of Novi Sad, Yugoslavia.

    1998-06-18: Distributional Description of Impulsive Gravitational Waves (invited). VIII Romanian Conference on General Relativity and Gravitation, Bistrita, Romania.

    1998-0-19: Gravitatonswellendetektoren für kosmologische Quellen. Gravity Seminar, Institute for Theoretical Physics, University of Vienna, (joint with S. Husa).

    1998-01-12: GR15-Konferenzbericht mit Überraschung. Gravity Seminar, Institute for Theoretical Physics, University of Vienna, (joint with S. Husa).

    1997-12-19: Geodesics and Geodesic Deviation for Impulsive Gravitational Waves. GR15 (15th International Conference on General Relativity and Gravitation), IUCAA, Pune, Indien.

    1997-10-14: Geodesics for Impulsive Gravitational Waves. Workshop "Nonlinear Theory of Generalized Functions", Erwin Schrödinger Institute, Vienna.

    1997-07-31: ELFI, A Gravitational Wave Detector for Cosmology. Gravity Seminar, Institute for Theoretical Physics, University of Vienna.

    1997-04-17,24: Distributionelle Krümmung von Strings. Gravity Seminar, Institute for Theoretical Physics, University of Vienna.

    1997-1-11, 18: Refined Algebraic Quantization. Gravity Seminar, Institute for Theoretical Physics, University of Vienna.

    1996-10-20: Symplektischer Formalismus für die Geometrodynamik. Gravity Seminar, Institute for Theoretical Physics, University of Vienna (joint with S. Husa and B. Pocza).

    1995-11-12: Colombeau Theorie und ultrarelativistischer Limes. Thesis Presentation, Institute for Theoretical Physics, University of Vienna.




    Mathematics Education and Public Outreach (Selection)



    2024-04-05: Neue Mathematik für die Schule. (mit Ilse Fischer), ÖMG-Fortbildungstagung für Lehrkräfte 2024, Universität Wien.

    2023-09-22: Neue Mathematik für die Schule. Kann die aktuelle mathematische Forschung einen Beitrag für den Mathematikunterricht leisten?
    (mit Ilse Fischer), eingeladener Vortrag beim ÖMG-Lehrer*innentag 2023 (Teacher's Day of the Austrian Mathematical Society), Graz, Austria.

    2023-07-18: Conceptions of student teachers on the limit concept. CERME13, Budapest, Hungary.

    2023-04-26: Von Schwarzen Löchern und dem Urknall. Popular talk at Vienna Planetarium.

    2022-08-31: Vorstellungen von zentralen mathematischen Begriffen beim Lernen und Lehren (mit Stefan Götz) GFD-ÖGFD-Tagung, Universität Wien.

    2022-04-22: Raumzeitsingularitäten. Die Theoreme von Penrose und Hawking. (eingeladener Hauptvortrag) ÖMG-Fortbildungstagung für Lehrkräfte 2022, Universität Wien.

    2021-04-09: Die Entzauberung des Unendlichen. ÖMG-Fortbildungstagung für Lehrkräfte 2021, Universität Wien.

    2020-09-29: Vorstellungen von Lehramtsstudierenden zum Grenzwertbegriff. GDM Onlinetagung, Würzburg, Germany.

    2019-04-03: Raumzeitsingularitäten. Popular talk at Vienna Planetarium. (Vortragsfolien auf Anfrage)

    2018-11-14: Gravitation und Raumzeitkrümmung. Popular talk at Vienna Planetarium.

    2018-05-17: Einführung in das mathematische Arbeiten: Überlegungen und Erfahrungen zur Studieneingangsphase. Universität Konstanz, Germany.

    2017-09-14: Wozu brauche ich das als Lehramtsstudierende/r? Bedarfsorientierte Gestaltung von Fachvorlesungen für Lehramtsstudierende. 19th International Congress of the Austrian Mathematical Society Salzburg, Austria.

    2015-10-13: Raumzeitkrümmung. Popular talk at the Austrian Academy of Science.

    2013-09-25: Zur Analysis-Ausbildung im Lehramtsstudium an der Universität Wien. 18th OEMG/DMV Congress, Innsbruck, Austria.

    2011-11-05: Einführung in das mathematische Arbeiten - der Passage Point an der Universität Wien. (gemeinsam mit Evelyn Suess-Stepancik) Khdm-Arbeitstagung "Mathematische Vor- und Brückenkurse: Konzepte und Perspektiven" Universität Kassel, Germany.

    2009-09-20: Überlegungen zum Einstieg ins Mathematikstudium: Einführung in das mathematische Arbeiten. 17th International Congress of the Austrian Mathematical Society, Technical University Graz, Austria.

    Teaching

    Teaching Activities

    My teaching activities cover a broad range of courses in mathematics as well as mathematical physics on all levels of the curriculum. Prevoiusly I have also been teaching courses in computer system administration and IT security.

    In mathematics I have been teaching many undergraduate courses on all kinds of topics while my graduate teaching predominantly is concerned with analysis and geometry, in particular, the theory of PDE, generalized functions, global analysis and differential geometry.

    I have coauthored with Hermann Schichl the beginners' textbook

    Einführung in das mathematische Arbeiten
    (Introduction into mathematical methodology)
    Springer Spektrum (Berlin, 2009, 2012, 2018)

    For the book and the corresponding project introducting an inductory phase for the mathematics curriculum, Hermann and I have been awarded the UNIVIE Teaching Award 2013 of Vienna University and the Ars Docendi 2016, the Austrian National Award in University Teaching. For related information you can have a look at     		EMA 3rd Edition


    To learn more on my teaching activities you can have a look at

    Courses

    • Einführung in das mathematische Arbeiten
      Springer Spektrum, 3. Auflage, Berlin, 2018
      gemeinsam mit Hermann Schichl
      Webseite zum Buch

    • Analysis für das Lehramt: Eine Einladung
      Sommersemester 2022
      Korrigierte Version 17-Juni-2022

    • Schulmathematik Analysis
      gemeinsam mit S. Kramer, E.Süss-Stepancik, Wintersemester 2022/23
      Version 17-Jan-2023

    • Alexandrov spaces
      jointly with Michael Kunzinger, Spring term 2018
      Version 1.0 (2021-01-25)

    • Riemannian Geometry
      jointly with Michael Kunzinger, Fall term 2020
      Version 1.0 (2021-04-16)

    • Lorentzian Geometry
      jointly with Michael Kunzinger, Spring term 2017 and 2021
      Version 1.0 (2024-04-22)

    • Grundbegriffe der Topologie
      Vorlesungsausarbeitung (SoSem 2015)

    • Analysiszyklus für LAK
      Vorlesungsausarbeitung (SoSem 2011--SoSem 2012)
    • Partielle Differentialgleichungen
      Vorlesungsausarbeitung (*) (SoSem 2010)

    • Theory of Distributions
      Lecture Notes, joint with Güther Hörmann (SoSem 2009)
      Draft Version (July 10, 2009)

    • Lokalkonvexe Vektorräume
      (Ausgewählte Kapitel aus Funktionalanalysis)
      Vorlesungsausarbeitung (*) (WS 2008/09)

    • Funktionalanalysis, Teil 2
      Vorlesungsausarbeitung (*) (SoSem 2008)

    • Funktionalanalysis, Teil 1
      Vorlesungsausarbeitung (*) (WS 2007/08)

    • Pseudo-Differentialoperatoren und mikrolokale Analysis
      (Ausgewählte Kapitel aus Partielle Differentialgleichungen)
      Vorlesungsausarbeitung (*) (WS 2006/07)

    • Distributionentheorie
      Vorlesungsausarbeitung (*) (SoSem 2006)

    • Grundbegriffe der Topologie
      Vorlesungsausarbeitung und Ausarbeitung der Proseminaraufgaben (*) (WS 2005/06)

    • Gewöhnliche Differentialgleichungen, Teil 1
      Vorlesungsausarbeitung und Ausarbeitung der Proseminaraufgaben (*) (SoSem 2005)

    • EDV und Mathematik
      Seminarausarbeitung (*)(SoSem 2004)

    • Kinetische Theorie (Existenztheorie des Vlasov-Poisson Systems)
      Seminarausarbeitung (*) (WS 2004/05)

    • Der Satz über implizite Funktionen
      Seminarausarbeitung (*) (WS 2004/05)

    • Technische Praxis der Computersysteme
      Vorlesungsskriptum Teil 1 (WS 2005/06), Teil 2-1 (SoSem 2005) Teil 2-2 (SoSem 2005)
      (Frühere Versionen Teil 1 (WS 2001/02) Teil 2 (SoSem 2002)


    (*) Per E-mail von den Autoren (Available via E-mail from the authors).

    Lecture Notes

    • Einführung in das mathematische Arbeiten
      Springer Spektrum, 3. Auflage, Berlin, 2018
      gemeinsam mit Hermann Schichl
      Webseite zum Buch

    • Analysis für das Lehramt: Eine Einladung
      Sommersemester 2022
      Korrigierte Version 17-Juni-2022

    • Schulmathematik Analysis
      gemeinsam mit S. Kramer, E.Süss-Stepancik, Wintersemester 2022/23
      Version 17-Jan-2023

    • Alexandrov spaces
      jointly with Michael Kunzinger, Spring term 2018
      Version 1.0 (2021-01-25)

    • Riemannian Geometry
      jointly with Michael Kunzinger, Fall term 2020
      Version 1.0 (2021-04-16)

    • Lorentzian Geometry
      jointly with Michael Kunzinger, Spring term 2017 and 2021
      Version 1.0 (2024-04-22)

    • Grundbegriffe der Topologie
      Vorlesungsausarbeitung (SoSem 2015)

    • Analysiszyklus für LAK
      Vorlesungsausarbeitung (SoSem 2011--SoSem 2012)
    • Partielle Differentialgleichungen
      Vorlesungsausarbeitung (*) (SoSem 2010)

    • Theory of Distributions
      Lecture Notes, joint with Güther Hörmann (SoSem 2009)
      Draft Version (July 10, 2009)

    • Lokalkonvexe Vektorräume
      (Ausgewählte Kapitel aus Funktionalanalysis)
      Vorlesungsausarbeitung (*) (WS 2008/09)

    • Funktionalanalysis, Teil 2
      Vorlesungsausarbeitung (*) (SoSem 2008)

    • Funktionalanalysis, Teil 1
      Vorlesungsausarbeitung (*) (WS 2007/08)

    • Pseudo-Differentialoperatoren und mikrolokale Analysis
      (Ausgewählte Kapitel aus Partielle Differentialgleichungen)
      Vorlesungsausarbeitung (*) (WS 2006/07)

    • Distributionentheorie
      Vorlesungsausarbeitung (*) (SoSem 2006)

    • Grundbegriffe der Topologie
      Vorlesungsausarbeitung und Ausarbeitung der Proseminaraufgaben (*) (WS 2005/06)

    • Gewöhnliche Differentialgleichungen, Teil 1
      Vorlesungsausarbeitung und Ausarbeitung der Proseminaraufgaben (*) (SoSem 2005)

    • EDV und Mathematik
      Seminarausarbeitung (*)(SoSem 2004)

    • Kinetische Theorie (Existenztheorie des Vlasov-Poisson Systems)
      Seminarausarbeitung (*) (WS 2004/05)

    • Der Satz über implizite Funktionen
      Seminarausarbeitung (*) (WS 2004/05)

    • Technische Praxis der Computersysteme
      Vorlesungsskriptum Teil 1 (WS 2005/06), Teil 2-1 (SoSem 2005) Teil 2-2 (SoSem 2005)
      (Frühere Versionen Teil 1 (WS 2001/02) Teil 2 (SoSem 2002)


    (*) Per E-mail von den Autoren (Available via E-mail from the authors).

    Students



    Current students

    • Sebastian Gieger
      Foundational topics in Metric Geometry and Lorentzian Length Spaces
      Ph.D. (co-supervisor R. Perales)

    • Miguel Prados Abad
      Topics in Non-Smooth Lorentzian Geometry
      Ph.D. (co-supervisors R. Perales, C. Rigoni)

    • Marta Salamo Candal
      Synthetic singularity theorems in General Relativity
      Ph.D. (co-supervisor M. Kunzinger)

    • Luca Mrini
      QG in nonsmooth Lorentzian spaces
      Ph.D. (co-supervisor C. Sämann)

    • Carl Rossdeutscher
      Marginally outer trapped tubes
      Ph.D. (co-supervisor W. Simon)

    • Matteo Calisti
      Metric geometry in the Lorentzian setting
      Ph.D.

    • Paul-Aaron Haberger
      The Geometry of Null surfaces
      M.Sc.

    • Gunter Wirthumer
      Conformal and causal boundaries
      M.Sc. (co-supervisor M. Kunzinger)

    Former students

    • Argam Ohanyan
      Singularity theorems and extensions of spacetime in low regularity
      Ph.D. 2024 (co-supervisor M. Kunzinger)

    • Tobias Beran
      Low regularity extensions of spacetimes, Lorentzian length spaces
      Ph.D. 2024 (co-supervisor M. Kunzinger)

    • Sebastian Gieger
      Volume comparison and singularities in General Relativity
      M.Sc. 2024 (co-supervisor M. Kunzinger)

    • Lisa Paradeisz
      Grundvorstellungen von LA-Studierenden zu Kernbegriffen der Analysis
      M.Ed. 2024

    • Katharina Steinau
      Unterrichtsmomente
      M.Ed. 2024 (co-supervisor C. Ableitinger)

    • Simon Reif
      Completeness of particle trajectories
      M.Sc. 2024

    • Moriz Lothar Frauenberger
      The Ehlers-Kundt conjecture
      M.Sc. 2024

    • Roman Brem
      Visibility of MOTs
      M.Sc. Physics 2023 (co-supervisor with W. Simon)

    • Benedict Schinnerl
      Non-regular spacetime geometry
      Ph.D. 2022

      Geodesics in low regularity
      M.Sc. 2018

      Konvergenz in topologischen Räumen (Convergence in topological spaces)
      B.Sc. 2016

    • Michaela Achleitner
      Grundvorstellungen zum Integralbegriff bei Lehramststudierenden
      M.Ed. 2022

    • Argam Ohanyan
      Geometric Foundations of the Classical Singularity Theorems
      M.Sc. (Physics, co-supervised by Stefan Palenta), 2022

      Splitting Theorems in Riemannian and Lorentzian geometry
      M.Sc. (Mathematics), 2020

    • Judith Painsi
      Surfing an impulsuive gravitational wave
      Diploma (teacher's curriculum), 2020

    • Carina Aschauer
      Der Satz von Gauß-Bonnet (The Gauß-Bonnet Theorem)
      Diploma (teacher's curriculumi), 2020

    • Dorian Cantele
      Mittelwertsätze
      B.Ed. 2020

    • David Binder
      Ausflug zu den äußeren Planeten
      B.Ed. 2019

    • Lukas Bäcker
      Unterrichtsmomente in der Lehramtsausbildung
      Diploma (teacher's curriculum), 2019

    • Arthur Sedivy
      Mathematische Grundlagen der Allgemeinen Relativitätstheorie (Mathematical Basics of General Relativity)
      Diploma (teacher's curriculum), 2017

    • Ronny Fischer
      Qualitative Theorie für planare dynamische Systeme (Qualitative theory for planar dynamical systems)
      Diploma (teacher's curriculum), 2017

    • Roman Pöll
      Ebene Kurven (Plane curves)
      Diploma (teacher's curriculum), 2017
      Privat-ORG Krems

    • Lukas Palme
      Überlagerungen (Coverings)
      B.Sc. 2017

    • Kathrin Peticzka
      Der Satz von Gauß-Bonnet (The Gauß-Bonnet Theorem)
      B.Sc., 2017

    • David Christa
      Geodesics on 2-manifolds
      B.Sc., 2016

    • Heyde Ye
      Unstetige Dynamische Systeme (Discontinuous dynamical systems)
      Diploma (teacher's curriculum), 2016

    • Daniela Huber
      Schnittstellenmodule in der Analysisausbildung (Interface modules in the Analysis curriculum)
      Diploma (teacher's curriculum), 2016

    • Helmut Geyer
      Totalkrümmung von Kurven (Total curvature of spacecurves)
      B.Sc. 2016

    • Josua Gruber
      Elementare Flächentheorie --- von den Grundlagen zur Krümmung (Classical Surfaces)
      Diploma (teacher's curriculum), 2013
      GRG3 Kundmanngasse

    • Rizwan Ahmad
      Multiplication of distributions
      Diploma, 2012

    • Clemens Hanel
      On singular wave equations
      Ph.D. 2011

      Linear hyperbolic second order partial differential equations on space time
      Diploma, 2006

    • Jan-Hendrik Treude
      Ricci curvature comparison in Riemannian and Lorentzian geometry
      Diploma in Theoretical Physics at University of Freiburg, Germany, 2011
      Ph.D. with Felix Finster at University of Regensburg
      Fachbereich Mathematik und Statistik, University Konstanz (Germany).

    • Stefan Fürdös
      Local Solvability of Pseudodifferential Equations
      Diploma, 2010
      Ph.D. at Vienna University with Bernhard Lamel
      University Brno (Czech Republic)

    • Nastasia Grubic
      Semi-Riemannian metrics of low differentiability
      Diploma in Mathematics and Theoretical Physics, 2010
      Ph.D. at Paris VI with Philipe LeFloch

    • David Rottensteiner
      Foundations of Harmonic Analysis on the Heisenberg group
      Diploma, 2010
      Ph.D at Imperial College with Michael Ruzhansky
      PostDoc at University of Vienna with Charly Gröchenig

    • Christina Schmidt
      On the sharp topology in algebras of generalized functions
      Diploma, 2008
      Business Analyst, Umweltbundesamt

    • Herwig Spornberger
      ODEs in a non-smooth setting
      Diploma, 2007
      Software developper

    • Eberhard Mayerhofer
      The wave equation on singular space times
      Ph.D, 2006 (co-advised with Michael Kunzinger)
      Mathematical Finance group, Dublin City University, Irland



    Vita

    Curriculum Vitae

    Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.

    Personal Data

    Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.

    Education

    Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.

    Scientific Career

    Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.

    Contact

    1. Mailing Address

      Fakultät für Mathematik, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria

    2. Office

      OMP1, Oskar-Morgenstern-Platz 1, Room 10.126

    3. Office hours

      by appointment

    4. Phone

      (+43 1) 4277-50682

    5. Fax

      (+43 1) 4277-9506

    6. E-Mail

      roland.steinbauer@univie.ac.at

    7. Website

      personal page, official university page