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, we will see further instances of this phenomenon, this time coming from geometry. In particular, I plan to explain the deformation theories of 

• flat connections on a smooth manifold, and
• complex structures on a smooth manifold.

In both cases, we will see that the deformations of a given structure are parametrized by the solutions to the Maurer-Cartan equation in a suitable dgla.