Groupoids and singular foliations

The proposed dissertation is centered around the differential geometry of singular foliations. While regular foliations are a classical subject in differential geometry, it is only about 10 years ago that a notion of singular foliation was developped that allows for the kind of constructions that have been carried out for regular foliations and, more general, for Lie algebroids. The first part of the dissertation should address certain invariants associated to singular foliations, such as their leaf space, isotropy groups, their holonomy representations, the associated C*- algebra...The study of these objects is still in a primordial phase, and an in-depth study is expected to lead to new, relevant results. The second part of the thesis should address some of the open problems about singular foliations, such as the linearization problem or determining if the holonomy representation is the 'shadow' of a higher groupoid representation. Finally, some of the results might have a counterpart in the more general setting of singular subalgebroids, and the dissertion should indicate for which results this is the case.status: publishe