Heat Kernels in Sub-Riemannian Settings

In this lectures we present a series of results concerning a class of diffusion second order PDE's of heat-type. The results we show have been obtained in collaboration with M.Bramanti, L.Brandolini and F. Uguzzoni (see [9], [10], [24]). The exended version of the main results presented in these notes is contained in [10]. © 2009 Springer-Verlag Berlin Heidelberg.