Orateur
Description
Origamis, also called square-tiled surfaces - are translation surfaces obtained by gluing finitely many copies of the unit square to each other along their boundaries. They are in particular closed Riemann surfaces. Their SL(2,Z)-orbit defines an algebraic curve in moduli space M_g, where g is the genus of the origami, which are special cases of Teichmüller curves.
The normalisation of a Teichmüller curve defined by an origami naturally comes with a Belyi morphism, i.e. a morphism to the sphere ramified over at most three points. This property equips the curve with a Grothendieck dessin d'enfants. We study these dessins in a special locus H(1,1), the stratum of translation surfaces of genus 2 with 2 singularities. For origamis in this locus, we can explicitly determine their Veech groups and leverage this information to describe the associated dessins d’enfants. This is joint work with Hannah Zeimetz.
