Translation surfaces are topological surfaces that when punctured are equipped with an atlas of local charts to the complex plane for which the transition functions are translations. This atlas gives us a well defined notion of whether or not a map from one translation surface to another has a constant Jocobian or is 'affine'. The Veech group of a translation surface is the group of Jacobians of orientation preserving affine self homeomorphisms of the surface. The size of this group can inform us on the dynamics (periodic/ergodic) of the geodesic flow in a given direction [Veech 1989].
Last spring I restricted to a certain class of translation surfaces, and introduced an infinite set of points on a toy translation surface whose stabilizer is the Veech group of our original surface. I will present the successful generalization of this construction to all translation surfaces, as well as demonstrate the need for only a finite subset of these points when testing all matrices up to a given Frobenius norm.