Research

I work in Mathematical General Relativity at the intersection of Lorentzian Geometry and Geometric Analysis of hyperbolic PDEs. I am particularly interested in low-regularity settings (which occur at interior and exterior boundaries, and interfaces) and develop new tools based on Differential Geometry and Metric Geometry.

lecture notes Publications

A complete list of publications is included below, with links to the preprints on arXiv , the (open access) published versions in the journals , and the final pdf versions . You can also visit the following external pages for more reviews etc.

Peer-reviewed articles

• A conformal Hopf-Rinow theorem for semi-Riemannian spacetimes, appeared online in Indagationes Mathematicae (2025), DOI 10.1016/j.indag.2025.01.004, 41 p.  arXiv  journal  pdf  video
• Time functions on Lorentzian length spaces, with L. García-Heveling, Ann. Henri Poincaré 26 (2025), no. 5, 1533–1572.  abstract  journal  pdf  video 
• Global hyperbolicity through the eyes of the null distance, with L. García-Heveling, Comm. Math. Phys. 405 (2024), no. 4, article number 90, 35 p.  arXiv  journal  pdf  slides  video 
• Properties of the null distance and spacetime convergence, with B. Allen, Int. Math. Res. Not. IMRN 2022, no. 10, 7729–7808.  arXiv  journal  pdf  slides  video 
• Variations of Weyl's tube formula, with G. Heckman, J. Geom. Anal. 31 (2021), no. 12, 11952–11970.  arXiv  journal  pdf  video 
• Weak second Bianchi identity for static, spherically symmetric spacetimes with timelike singularities, with M. K.-H. Kiessling and A. S. Tahvildar-Zadeh, Classical Quantum Gravity 38 (2021), no. 18, 185001, 31 p.  arXiv  journal  pdf  slides 
• Inscribed radius bounds for lower Ricci bounded metric measure spaces with mean convex boundary, with C. Ketterer, R. J. McCann, and E. Woolgar, SIGMA 16 (2020), 131, 29 p.  (Special Issue on Scalar and Ricci Curvature in honor of Misha Gromov on his 75th Birthday)  arXiv  journal  pdf 
• Initial data and black holes for matter models, in "Hyperbolic Problems: Theory, Numerics, Applications", by Alberto Bressan, Marta Lewicka, Dehua Wang, Yuxi Zheng (Eds.), AIMS Ser. Appl. Math., vol. 10, 336–345, Am. Inst. Math. Sci. (AIMS), Springfield, MO, 2020.  arXiv  article pdf  book  meeting 
• On the asymptotic behavior of static perfect fluids, with L. Andersson, Ann. Henri Poincaré 20 (2019), no. 3, 813–857.  arXiv  journal  pdf 
• Hyperboloidal evolution and global dynamics for the focusing cubic wave equation, with R. Donninger, Comm. Math. Phys. 353 (2017), no. 2, 549–596.  arXiv  journal  pdf  poster 
• Length structures on manifolds with continuous Riemannian metrics, New York J. Math. 21 (2015), 273–296.  arXiv  journal  pdf  slides 
• The formation of trapped surfaces in spherically-symmetric Einstein-Euler spacetimes with bounded variation, with P. G. LeFloch, J. Math. Pures Appl. 102 (2014), no. 6, 1164–1217.  arXiv  journal  pdf  slides  video 
• New energy inequalities for tensorial wave equations on spacetimes that satisfy a one-sided bound, with J. D. E. Grant and P. G. LeFloch, Comm. Partial Differential Equations 37 (2012), no. 9, 1596–1619.  arXiv  journal  pdf  poster 
• Tectonic geomorphological investigations of antiforms using differential geometry: Permam Anticline, northern Iraq, with M. Frehner and B. Grasemann, AAPG Bulletin 96 (2012), no. 2, 301–314.  journal  pdf  poster  code 
• Algebras of generalized functions with smooth parameter dependence, with M. Kunzinger, Proc. Edinburgh Math. Soc. (2) 55 (2012), no. 1, 105–124.  arXiv  journal  pdf 
• An algebraic approach to manifold-valued generalized functions, Monatsh. Math. 166 (2012), no. 3-4, 361–370.  arXiv  journal  pdf 

Non-peer-reviewed articles, proceedings, reports etc.

• Local and global properties of the null distance, Oberwolfach Rep. 21 (2024), no. 3, 2045–2048.  proceedings  proceedings pdf  meeting 
  
• Matter particles, naked singularities, and a weak second Bianchi identity, Oberwolfach Rep. 18 (2021), no. 3, 2231–2233.  proceedings  proceedings pdf  meeting 
• Singularity formation for perfect fluids with linear equation of state, Oberwolfach Rep. 17 (2020), no. 4, 2104–2106.  proceedings  proceedings pdf  meeting 
• LehrFEM - A 2D Finite Element Toolbox, with contributions by Patrick Meury and Eivind Fonn, Manual for FEM MATLAB code (Sep 2008), ETH Zürich, 118 p.  pdf  code 

Theses

• Analytic and geometric aspects of spacetimes of low regularity, PhD thesis in Mathematics (2014), Université Pierre et Marie Curie (Paris 6) and University of Vienna.  thesis AT_at  thesis FR_fr  abstract 
• Curvature analysis of anticlines in the Zagros mountains (Iraq), Bachelor thesis in Earth Sciences (2010), University of Vienna.  pdf  MATLAB code 
• Isomorphisms of algebras of smooth and generalized functions, Diploma/Master thesis in Mathematics (2009), University of Vienna. thesis  pdf 

grants Projects

Current projects

Spacetimes near the boundary of existence
Vidi project VI.Vidi.233.024 supported by the Dutch Research Council (NWO)
PI · 2025–2030 · 850 k€

Emergence at all scales
Consortium NWA.1630.23.007 supported by the Dutch Research Council (NWO)
co-PI · 2025–2030 · 7.1 M€

A new geometry for Einstein's theory of relativity & beyond
Emerging fields program supported by the Austrian Science Fund (FWF)
international project partner · 2024–2029 · 7 M€

Completed projects

• Nonsmooth spacetimes and singularities · NWO Veni project VI.Veni.192.208 · PI · 2019–2023 · 280 k€
• Lorentzian curvature revisited · ESI Junior Research Fellowship for extended research stay · PI · Jul–Aug 2017
• A synthetic approach to spacetimes of low regularity · L’Oréal "For Women in Science" Fellowship · PI · 2012–2013 · 20 k€
• Spacetimes of low regularity · Bourse d'excellence Eiffel · PI · 2011–2012 · 15 k€
• Analysis of singular geometric structures · Forschungsstipendium University of Vienna · PI · 2010 · 13 k€

team Team

Current team members

• Thijs de Kok · PhD candidate (funded by my Vidi grant) · 2025–2029
• Tomás O'Shea · PhD candidate (funded by the Emergence consortium, co-supervised with R. Loll) · 2025–2029
• Jakob Hedicke · REI Postdoctoral Fellow · 2025–2027

Former team members

• Leonardo García Heveling · PhD thesis "Causality and Time in Non-smooth Lorentzian Geometry"   · 2019–2023
• Elefterios Soultanis · REI Postdoctoral Fellow · 2021–2022

Collaborators

Brian Allen, Lars Andersson, Roland Donninger, Marcel Frehner, Leonardo García-Heveling, James D.E. Grant, Bernhard Grasemann, Gert Heckman, Christian Ketterer, Michael K.-H. Kiessling, Michael Kunzinger, Philippe G. LeFloch, Robert J. McCann, A. Shadi Tahvildar-Zadeh, Eric Woolgar