Minicourse: Differential forms and homotopy groups

De Rham's classical theorem says that differential forms on a smooth manifold M can be used to compute the real cohomology of M. Can differential forms be used to compute non-trivial information about homotopy groups of M? I will show how differential forms can be used to compute information about the "non-abelianess" of the fundamental group of M and will prove Chen's de Rham theorem for the fundamental group.