Lie Methods in Deformation Theory

Deformation theory is an important subject in algebra and algebraic gemetry, whose origin dates back to Kodaira, Spencer, Kuranishi, Gerstenhaber and Grothendieck. In the last 30 year a new approach, based on some ideas from rational homotopy theory, has permitted non only to solve some long standing open problems, but also to clarify the general theory and to relate apperently different features. This approach works over a field of characteristic 0 and the central role is played by the notions of differential graded Lie algebra and L-infinity algebra.