Dealing with pseudo-holomorphic disks, $A_\infty$-algebras supply a convenient working language. In particular, solutions to the Maurer-Cartan equation, a.k.a. bounding chains, allow us to describe bubbling at the boundary. Such bubbling is an obstacle for defining structures related to Lagrangians, such as Floer cohomology or open Gromov-Witten invariants.

In my talk I will define, following Fukaya's approach, an $A-\infty$ structure on the ring of differential forms on a Lagrangian, and explain the suitable Maurer-Cartan equation. I will explain the use of bounding chains in defining open Gromov-Witten invariants. As time permits, I will elaborate on the construction of a bounding chain, and how this explains the geometric meaning of the objects counted by the open Gromov-Witten invariants.

This is joint work with Jake Solomon.

No previous knowledge of any of the objects mentioned above will be assumed.