Cyclic homology of Fukaya categories and the linearized contact homology

In this talk I will show that for an exact symplectic manifold M with vanishing first Chern class,
the cyclic cohomology of the Fukaya category of M has an involutive Lie bialgebra structure.
If M has an contact type boundary, then there is a Lie bialgebra homomorphism from the
cyclic cohomology to the linearized contact homology of M. We will also explain our result
from the topological conformal field theory point of view, and if time permits, relate it with
string topology.