In our group, various topics in condensed matter theory are investigated. Generally we are interested in the fundamental question of how the properties of complex many-body systems can be described: examples of such systems are the electrons in a solid, and the atoms in liquid helium. In several cases, these systems show, at low temperatures, a phase transition into a novel state, for example, from a metal to an insulator, or from a normal liquid to a superfluid. Our goal is to develop simple models for such phenomena, study these models with analytical and numerical methods, and relate the theoretical results with experimental observations.