From Lie groupoids to resolutions of singularities. Applications to   symplectic and Poisson resolutions
  We use the techniques of integration of Poisson manifolds into symplectic Lie groupoids to build symplectic resolutions (= desingularizations) of the closure of a symplectic leaf. More generally, we show how Lie groupoids can be used to lift singularities, in particular when one imposes a compatibility condition with an additional structure given by a multi-vector field. 
Camille Laurent-Gengoux