We establish the deformation theory of Lie groupoid morphisms, describe the corresponding
deformation cohomology of morphisms, and show the properties of the cohomology. We …

We extend classical Morse theory to the realm of Lie groupoids and their differentiable
stacks. This allows us to obtain both topological and geometrical information of the singular …

In this work we discuss an approach to describe the dynamics of fluid flows with vortex
sheets using a framework of geodesics on a certain Lie groupoid of volume-preserving …