Kaj Börjeson: Differential operators and homotopy algebra.

Batalin-Vilkovisky algebras are graded commutative algebras with a square-zero differential operator of order 2. There is a Lie bracket measuring how this fails from being a derivation. In general we have a whole family of conditions that create an L-infinity structure. I will talk about what happens when we drop the commutativity and how this leads to A-infinity structures as well as examples of "non-commutative Batalin-Vilkovisky algebras.