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These notes are the basis of a course given at the Institut Henri Poincare inSeptember 2014. We survey some recent results related to the geometric analysisof hypoelliptic diffusion operators on totally geodesic Riemannian foliations.We also give new applications to the study of hypocoercive estimates forKolmogorov type operators.

Sub-Laplacians and hypoelliptic operators on totally geodesic Riemannian foliations