Mathematics

the aim of the talk is to describe the classical notion of (infinitesimal) deformations  of an affine scheme over a field of characteristic 0 entirely in terms ofthe model structure in the category of nonpositively graded differential graded commutative algebras.This allows to define naturally  the notion of deformation of an affine DG-Scheme, even over a DG-Artin ring, extending the classical case and in accord with the general principle that ``deformations are controlled by the DG-Lie algebra of derivations of a cofibrant resolution''.