For each acyclic quiver Q we define a complex affine variety X(Q) called frieze variety. It is the Zariski closure of a set of points defined recursively. From a more conceptual viewpoint, the coordinates of these points are specializations of preprojective cluster variables in the cluster algebra associated to Q. In the talk I will explain the result that Q is representation finite, tame, or wild if and only if dim X(Q) is 0,1, or greater than 1, respectively. Speaker(s): Li Li (Oakland University)