Geometric analysis on stratified spaces

Stratified spaces are metric spaces that have been introduced first in the context of topology (H.~Whitney, R.~Thom), and later have been studied from an analytical point of view (J.~Cheeger, R.~Melrose, R.~Mazzeo...), as a generalization of isolated conical singularities. They also appears as quotients or limits of smooth Riemannian manifolds. In this talk I will give an introduction to the setting of stratified spaces and describe some geometric analysis results related to the spectrum of the Laplacian and Sobolev inequalities.