URegina Topology & Geometry Seminar: Francis Bischoff

In this seminar, we have seen that problems in deformation theory are often controlled by differential graded Lie algebras (dgla). For example, in Martin's talk, we saw how the deformations of an associative algebra are controlled by a dgla structure on the Hochschild cochain complex. In this talk and the next, will see an instance of this phenomenon coming from geometry: the theory of flat connections on a smooth manifold.

In part 2, we will see that the deformations of flat connections on a smooth manifold are parametrized by the solutions to the Maurer-Cartan equation in a suitable dgla.