Deformations of Lie groupoids

In this talk we discuss deformations of Lie groupoids and introduce the cohomology which controls them. We then study some of its properties, and give a geometric interpretation for it in low degrees. We will also look at relations with other cohomologies: deformation cohomologies for classical examples, such as Lie group actions and foliations, and deformation cohomology of Lie algebroids. We then explain how to use the deformation cohomology in order to prove rigidity and normal form results for compact and for proper Lie groupoids. This talk is based on joint work with Marius Crainic and Ivan Struchiner.