Closure of singular foliations: the proof of Molino's conjecture

A singular foliation on a Riemannian manifold M is called Riemannian if their leaves are locally equidistant.  A typical example of a singular Riemannian foliaton is the decomposition of  M into the orbits of an isometric group action on M. Another example is the holonomy foliation, the foliation whose leaves are orbits of parallel transports on an Euclidean vector bundle with a metric connection. In this talk we review some basic concepts and examples and give an ideia of the proof of Molino's conjecture that for each singular Riemannian foliation  the partition given by the closure of the leaves is again a singular Riemannian foliation.  This talk is based on a joint work with Prof. Marco Radeschi (Notre-Dame)