This project aims to develop new tools for the description and understanding of microlocal properties in generalized function algebras. Our investigation will combine modern techniques from functional analysis and nonstandard analysis. We will apply the new tools to study hyperbolic partial dierential equations with highly singular coecients and data as they appear e.g. in seismology. For such equations, classical microlocal methods fail. We will in particular investigate the qualitative behaviour of solutions to such equations.

Our concrete goals are:

• Introduce techniques from nonstandard analysis to describe wave front sets.
• Investigate the role of Baire techniques in generalized function algebras.
• Apply the newly introduced techniques to hyperbolic problems of current interest.