A-infinity algebras arise whenever one has a multiplication which is "associative up to homotopy". There is an important theory of minimal models which involves studying differential graded algebras via A-infinity structures on their homology algebras. However, this only works well over a ground field. Recently Sagave introduced the more general notion of a derived A-infinity algebra in order to extend the theory of minimal models to a general commutative ground ring.
Operads provide a very nice way of saying what A-infinity algebras are - they are described by a kind of free resolution of a strictly associative structure. I will explain the analogous result for derived A_infinity algebras - these are obtained in the same manner from a strictly associative structure with an extra differential.
This is joint work with Muriel Livernet and Constanze Roitzheim.
- Topology Seminar