# Research project: With origamis to Teichmüller curves in moduli space

**funded by the Eliteprogramm für Postdoktorandinnen**

**und Postdoktoranden der Landesstiftung Baden-Württemberg**

In this project, we investigate Teichmueller curves coming from origamis. In particular, we are interested in their algebraic and geometric properties, their position in the moduli space, their intersection behaviour and their Veech groups as subgroups of SL(2,Z).

# People in the project

# Events

- Weihnachtsworkshop 2008: December 15 to 17
- Talk on
**Non discrete and non finitely generated Veech groups**by Ferran Valdez (MPI Bonn), July 17 2008 in the*Mathematischen Kolloquium der Fakultät* - Talk on
**Counting trajectories for rectangular billiards and counting pillow covers**by Jayadev Athreya (Princeton University), May 29 2008 in the*Mathematischen Kolloquium der Fakultät* - Weihnachtsworkshop 2007

# Related links

- ... more on origamis
- Research on origamis in Karlsruhe
- Website of the Workgroup Number Theory and Algebraic Geometry
- A short description of the project
- Website of our project at Landesstiftung Baden-Württemberg
- Website of Landesstiftung Baden-Württemberg
- A wiki for translation surfaces: Wild Translation Surfaces Project

# Project description

We investigate algebraic curves in the moduli space of curves or that are described by few combinatorial data - thanks to so called *origamis* or *square tiled surfaces*. These curves are called origami curves and they are special cases of Teichmueller curves. Every Teichmueller curve is characterized by its Veech group, a discrete subgroup of SL(2,R) that is at the same time a subgroup of the mapping class group.

Although the construction principles for origami curves are very simple and there is even an algorithm that determines the Veech group of a given origami, very little is know today about these curves: what are their common properties and their fields of definition? What is their position in the moduli space?

*Workgroup Number Theory and Algebraic Geometry*

*Institute for Algebra and Geometry*

*Universitaet Karlsruhe*

*76128 Karlsruhe*

*Germany*