[Abstract homotopy theory seminar] Computing cohomology of differentiable stacks

The notion of a differentiable stack in geometry can be used to study objects such as orbifolds, moduli spaces or classifying spaces, which despite not being manifolds carry similar differential geometric information. Examples in particular include quotients of manifolds by a Lie group action. These objects are closely related to equivariant cohomology, a cohomology theory on such manifolds with group actions that has many applications in different areas of mathematics and physics. It can be seen as a special case of the cohomology of differentiable stacks. The main tool for computing equivariant cohomology, the Cartan model, has no equivalent in the full generality, but there have been recent advances on similar constructions.