Title: Models for differentiable stack cohomology - A journey via equivariant cohomology and Lie groupoids
Abstract: Equivariant cohomology is a cohomology theory for manifolds (or
generally topological spaces) with a Lie group action. We can also
interpret equivariant cohomology as the cohomology of the differentiable
stack presented by the action groupoid. This poses the question if the
Cartan model for equivariant cohomology can be generalised to a model
for differentiable stack cohomology. I will review the problem and some
of the known strategies on it and give insights into my PhD project on
the topic. I aim to motivate why connections on the Lie algebroid play a
distinct role and how a certain type of multiplicative Ehresmann
connection appears in the theory.
