Professor Marcos M. Alexandrino

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 A singular foliation is called a singular Riemannian foliation (SRF) if every geodesic that is perpendicular to one leaf is perpendicular to every leaf it meets. A typical example of such a foliation is the partition of a manifold into the orbits of an isometric action. On one hand, recent techniques in the theory of SRF shed light on some questions about isometric actions. On the other hand, the theory of isometric actions feeds the other theory with examples and motivates new questions. Furthermore, as stressed in the book of Gromoll and Walschap, "in the last decades there has been increasing realization that these foliations play a key role in understanding the structure of Riemannian manifolds, particularly those with positive or nonnegative sectional curvature". Last, but not least, the quotient space of SRF or isometric actions provide examples of natural metric spaces with several interesting properties.

 In our research we explore some of these connections, and discuss, among other things, quotient spaces, generalizations of Riemannian submersions, relations between topology of the ambient space and topological invariants of foliations. For more information see our book or our papers.