Abstract:We will recall the definitions of cluster algebras and of presymplectic 2-forms compatible with cluster algebra structure. Such forms are associated with quivers. Mutation of cluster algebra leads to mutation of quivers. All quivers that are obtained by mutation sequences from a given one form the mutation class of the given quiver. In the talk we will describe quivers whose mutation class is finite. We will outline also the approach to the classification of cluster algebra by its growth.
This is a joint work with A.Felikson and P.Tumarkin.