I am interested in the development of the interface between general relativity and bifurcation theory. This field uses tools and methods from bifurcation theory, singularity theory, catastrophe theory, dynamical systems, as well as general relativity and its various geometric extensions. A main purpose is to study problems related to cosmology, black holes, and other areas, with methods of bifurcation theory. Usually this also leads to a need for new techniques in bifurcation theory itself.