Characteristic classes of A-infinity algebras

There is a construction, due to Kontsevich, which produces cohomology classes in moduli spaces of Riemann surfaces from the initial data of an A-infinity algebra with an invariant inner product -- a kind of homotopy theoretic notion of a Frobenius algebra.

In this talk I will describe a version of this construction based on noncommutative symplectic geometry and use it to show that homotopy equivalent A-infinity algebras give rise to cohomologous classes. I will explain how the whole framework can be adapted to deal with Topological Conformal Field Theories in the sense of Costello, Kontsevich and Segal.