This research group supported by Neumann Institute for Computing and the GSI in Darmstadt works jointly with members of the lattice group at GU-Frankfurt on the properties of the strong interactions under extreme conditions. In particular, the long term goal is to determine the phase diagram of QCD as a function of temperature and baryon density, as well as the properties of matter in the hadron and quark gluon plasma phases directly from numerical simulations of lattice QCD.