Mathematics

Translation surfaces are oriented surfaces equipped with an atlas of local charts to R^2 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 is affine (linear plus a translation). The Veech group of a translation surface is the group of Jacobians of orientation preserving affine automorphisms of the surface. The size of this group can inform us on the dynamics (periodic/ergodic) of the geodesic flow [Veech 1998]. I will discuss an algorithm for computing generators of a Veech group based in part on the observation that such automorphisms permute the lines connecting the singularities of the surface.