## Research

### Research topics of the working group:

Teichmüller curves and Veech groups.

Translation surfaces, in particular origamis/square-tiled surfaces.

Subgroups of the automorphism group Aut(F_n) and the outer automorphism group Out(F_n), Culler-Vogtmann outer space, connection between Teichmüller space and outer space.

### SFB TRR 195 Symbolic Tools in Mathematics and their Application:

Since 2017 our working group is part of the SFB TRR 195 with the project Algorithmic Approaches to Teichmüller curves.

### Seminar of Algebra and Number Theory

The Seminar of Algebra and Number Theory takes place on Monday afternoon. More information including a list of past and forthcoming talks can be found on the web page of the Seminar.

### Weihnachtsworkshop on Geometry and Number Theory

Traditionally, the Cristmas Workshop takes place once a year in the last week before Christmas. Please find more information here and the here.

### Software

The following software is or was developed by members of our group:

- Direct access to the Origami-Database.
- GAP package ModularGroup
- GAP package Origami
- ArangoDB Origami Database.
- SAGE program Lipschitz Calculator CV_n
- C++ program Origami-Library calculates the Veech group of an origami. Developed in Karlsruhe together with Karsten Kremer.
- Python program Origami-Visualize draws nice images of origamis. Developed by Joachim Breitner in Karlsruhe. There's also some sample input and an example TeX file.