Globally hyperbolic Lorentzian manifolds with special holonomy Helga Baum, Humboldt University of Berlin Lecture at the 2006 IMA Summer Program: Symmetries and Overdetermined Systems of Partial Differential Equations, Minnessota, July 17-August 4, 2006 Before I start with the topic in the title, I will explain how this topic is related to the subject of the Summer Program and to some other talks during the workshop (Cooperation with I. Kath, F. Leitner, Th. Leistner, Th. Neukirchner, A. Galaev, O. M¨ uller) 1