Crystal operators on tropical points of cluster varieties

The unipotent radical U of a Borel subgroup of SL_n(C) posses the structure of a Cluster Variety. Gross-Hacking-Keel-Kontsevich constructed a canonical basis B of the coordinate ring C[U]. The basis B is parametrized by a cone K in the tropical points of a dual cluster variety. In this talk we introduce certain operators on K generating the cone recursively. As a consequence we obtain a crystal structure on B in the sense of Kashiwara.