Disordered systems are a central subject in many areas of physics, including condensed-matter physics, optics, acoustics, seismology, and atomic physics. It is more active than ever, with landmark results obtained in the very recent years. This progress paves the way to new challenges. In particular, the question of the combined effects of disorder and interactions is one of the most challenging problems that one has to face in quantum systems.

In condensed-matter physics this question has been intensively studied. For non-interacting systems, disorder leads to Anderson localization. Interactions have been shown to induce dramatic corrections to the noninteracting case, which are not fully understood. The combined effects of disorder and interactions are very rich as they depend on the nature of the system (fermions, or bosons, such as cooper pairs in a superconductor) and on the dimension of the system. Many experimental realizations of disordered systems have been studied such as disordered semiconductors, disordered superconducting films, Josephson junction arrays, disordered magnets, etc. Despite the important progress accomplished both on the theoretical and on the experimental fronts, many important questions remain, testifying to the complexity and the richness of the problem.

Recently, ultracold atomic gases have provided very controlled systems, in which to investigate a variety of fundamental questions, with new tools, new viewpoints, and thus new challenges. In these systems, disorder can be introduced in a very controlled way using speckle patterns or bichromatic lattices. Ultracold atomic systems have also the advantages to be able to produce bosonic or fermionic systems, and even mixtures of the two. Recently spectacular observation of Anderson localization of matterwaves was reported in such systems, and several investigations of the combined effect of disorder and interactions have been or are currently being performed as well.

Meeting of the two communities and sharing of expertise and results is the aim of the two-week this Summer School. It is primarily targeted to young researchers but definitely also to more experienced researchers. We certainly expect a very strong cross fertilization of ideas, both on the experimental and on the theoretical side by putting the two communities together.

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