String theory compactifications have recently focused on internal spaces which are not ordinary manifolds or orbifolds but more general structures (e.g. so-called T-folds or non-geometric backgrounds), as are naturally implied by dualities in flux compactifications. These ‘generalized geometries’ connect complex and symplectic geometry and are also under investigation by mathematicians. As string theory provides a model of quantum gravity, such generalized geometries belong to the scientific spectrum of the RTG and merit a research topic. Generalized geometry furthermore provides a systematic approach to the construction of classical models of gravity