Research

Research Topics

I was originally trained as a mathematical physicist specializing in general relativity. Over the years I have developed 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

  • spacetime singularities & cosmic censorship,
  • non-smooth spacetime geometries, and
  • exact radiative spacetimes, in particular impulsivge gravitational waves.

    • Mathematical Analysis

  • (non-linear) generalized functions,
  • the theory of PDEs, in particular kinetic theory, and
  • time frequency analysis & modulation spaces.

    • Mathematics Education Research

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

Most of my research is carried out within the Austrian Science Fund's (FWF) Emerging Fields project A new geometry for Einstein's Theory of Relativity and Beyond with my long-term colleague and collaborator Michael Kunzinger, as well as Raquel Perales, Chiara Rigoni, and Clemens Sämann.

Much of my earlier 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