We study the small-time asymptotics of the heat kernel associated with a sub-Riemannian Laplace operators. The nilpotentisation method uses the (pointwise) dilations associated with the structure to obtain an expansion that is valid in a shrinking neighbourhood of the diagonal. For singular structures, the weights of the dilation may vary from one point to the other and the previous method needs to be improved.
Joint work with Yves Colin de Verdière and emmanuel Trélat.
