Veech groups of origami that are congruence groups

Vortrag von Prof. Dr. Gabriela Weitze-Schmithüsen

Sprecher eingeladen von: Prof. Dr. Corinna Ulcigrai

Datum: 28.11.22  Zeit: 13.30 - 14.30  Raum: Y27H28

Origamis are special translation surfaces which are obtained as patchwork from finitely many Euclidean squares. An important algebraic invariant is their Veech group which is a finite index subgroup of \(SL(2,\mathbb{Z})\). It is unknown which subgroups of \(SL(2,\mathbb{Z})\) occur as Veech groups. However for congruence groups of prime level there is a constructive approach which shows that all but five special cases occur. We find four of the missing five cases and study the question whether the result can be generalized to general congruence groups. The question is intimately related to the study of orbit spaces of \(SL(2,\mathbb{Z}/n\mathbb{Z})\).