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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. My current research interests include but are not confined to the following list:

• Algebras of generalized functions and their applications
  • structure theory of algebras of generalized functions
  • geometric aspects
  • applications in geometric situations, in particular to general relativity
  • applications in PDE, in particular regularity theory
    
    
• General relativity
  • Semi-Riemannian geometry with metrics of low regularity
  • singularity theorems and cosmic censorship
    
    
• Nonlinear PDE/Kinetic Theory
  
  
• Time frequency analysis/Modulation spaces

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

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

• a brief desription of my research topics
• my list of publications and preprints
• my list of talks, and
• a list of research projects I have contributed to.