Gabriela Schmithüsen

Origamis are a special class of translation surfaces which are obtained by the following handy construction: Take finitely many Euclidean unit squares and glue them along parallel edges via translations such that you obtain a surface. The study of the moduli spaces of translation surfaces of fixed genus has been an important goal for the last twenty years. A crucial invariant of a translation surface is its Veech group which is a discrete subgroup of SL(2,R). In the case of origamis these groups are finite index subgroups of SL(2,Z). We present congruence properties of them and generalizations to other classes of so-called imprimitive translation surfaces.