Many deformation problems in algebra and geometry are controlled by DG (differential graded) Lie algebras. The Deligne groupoid associated to a nilpotent DG Lie algebra (introduced in 1988 in a paper by Goldman-Millson) classifies deformations and gauge equivalences between them.

In a recent paper I introduced the reduced Deligne groupoid, which allows the treatment of unbounded DG Lie algebras. My work also applies to pronilpotent DG Lie algebras.

In this talk I will explain the definitions and results mentioned above, and will also briefly discuss L-infinity quasi-isomorphisms.

For full details see the lecture notes http://www.math.bgu.ac.il/~amyekut/lectures/MC-complete/notes.pdf or the paper arXiv:1103.1035.