## Submitted by:

The Seiringer group develops new mathematical tools for the rigorous analysis of many-particle systems in quantum mechanics, with a special focus on exotic phenomena in quantum gases, like Bose-Einstein condensation and superfluidity.

A basic problem in statistical mechanics is to understand how the same equations on a microscopic level lead to a variety of very different manifestations on a macroscopic level. Due to the intrinsic mathematical complexity of this problem, one typically has to resort to perturbation theory or other 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 necessary to develop new mathematical techniques and methods. These new methods lead to different points of view and thus increase their understanding of physical systems. Concrete problems under current investigation include the spinwave approximation in magnetism, the validity of the Bogoliubov approximation for the excitation spectrum of dilute Bose gases, and pattern formation in Ising models with competing interactions.