Cluster Algebras and Mirror Symmetry

I will reformulate the theory of cluster algebras in terms of birational geometry of Calabi-Yau manifolds, from which the Laurent Phenomenon will be transparant, and then indicate how the Fock-Goncharov conjectures on canonical dual bases are a special case of our mirror symmetry conjecture discussed in the colloquim, and deduce from this a necessary and sufficient condition for the Fock-Goncharov conjecture (for the X-space) to hold when the associated skew symmetric matrix is rank two. No previous knowledge of cluster algebras is required.