Examples of classifications of the stack of perverse sheaves

The aim of this talk is to show how the stack theory can be used to glue description of the category $\mathcal{P} erv_X$ of perverse sheaves on a stratified space $X$. First at all, I'll recall the equivalence, due to Galligo Granger Maisonobe, between the category $\mathcal{P} erv_{\mathbb{C}^n}$ and a category of quiver's representations. Then I'll recall the definition of a stack and I'll give a characterization of the 2-category of stack on $\mathbb{C}^n$. This is allow me to define a stack on $\mathcal{C}^n$ equivalent to the stack of perverse sheaves on $\mathbb{C}^n$. Finally I'll show how this construction can be used to give descriptions of the category $\mathcal{P} erv_X$, where $X$ is $\mathbb{C}^2$ stratified by a generic lines arrangement or a smooth toric variety.