Our research focuses on many-body systems in quantum mechanics. In particular, we are interested in problems in quantum statistical mechanics and condensed matter physics. Such systems display a rich variety of complex phenomena, and it is of fundamental importance to understand the basic underlying principles as thoroughly and precisely as possible.

The goal of our research is the development of new mathematical tools for a rigorous analysis of such quantum many-body systems. Because of the complexity of the systems many phenomena are so far only understood using either perturbation theory or uncontrolled approximations whose justification remains open. It therefore remains a challenge to derive non-perturbative results and to obtain precise conditions under which the various approximations can or cannot be justified. For this purpose it is often necessary to apply modern mathematical techniques or even to develop new ones. In this way, physical ideas and intuition tend to give rise to new mathematical methods. These new methods lead to different points of view and thus increase our understanding of physical systems.