My fields of interest are Veech groups of translation surfaces and Teichmüller curves in moduli spaces. I have particularly worked on special cases that arise from coverings of elliptic curves that are ramified over at most one point, called square tiled surfaces or origamis.
This work lead me to the study of subgroups of mapping class groups, of subgroups of the automorphism group Aut(F_n), Out(F_n) and GL(n,Z) and the Culler-Vogtmann outer space. I am especially interested in relations between Teichmüller spaces and outer spaces.

Since summer 2007: Research project With origamis to Teichmüller curves in moduli space.

More informations about our research on origamis in Karlsruhe: Origamis in Karlsruhe

• An algorithm for finding the Veech group of an origami. Experimental Mathematics 13, No.4, 459-472 (2004).
• Veech Groups of Origamis PhD Thesis Karlsruhe 2005. (PS version/PDF version)
• Examples of origamis. Proceedings of the III Iberoamerican Congress on Geometry. In: The Geometry of Riemann Surfaces and Abelian Varieties. Contemp. Math. 397, 2006 (p. 193 – 206).
• On the boundary of Teichmüller disks in Teichmüller and in Schottky space. Together with F. Herrlich. Handbook of Teichmueller theory. Ed. A. Papadopoulos, European Mathematical Society, 293 -- 349 (2007).
• Origamis with non congruence Veech groups. In Proceedings of Symposium on Transformation Groups, Yokohama, November 2006.
• A comb of origami curves in the moduli space M_3 with three dimensional closure. Together with F. Herrlich. Geometriae dedicata 124, 69 -- 94 (2007).
• An extraordinary origami curve. Together with F. Herrlich. Mathematische Nachrichten 281, No. 2, 219 -- 237 (2008).
• Dessins d'enfants and origami curves. Together with F. Herrlich. Handbook of Teichmueller theory II. Ed. A. Papadopoulos, European Mathematical Society, 767 -- 809 (2009).
• A origami of genus 2 with a translation. Together with F. Herrlich and A. Kappes. Preprint.
• Infinite translation surfaces with infinitely generated Veech groups. Together with P. Hubert. Preprint.
• Veech groups of Loch Ness monsters. Together with Piotr Przytycki and Ferran Valdez. Accepted to Annales de l'Institut Fourier.

• Christmas-Workshops in Geometry and Number Theory

• Group theory with Rubik's cube
• Knot-theory for all ages (sorry only in German)
• Mathematics on Billiard Tables: a public lecture in German together with Prof. Dr. F. Herrlich within the program for the Year of Mathematics 2008