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 can be found here: Origamis in Karlsruhe
Since Summer 2009: Research project Culler and Vogtmann's outer space and Out(F_n) - geometric and algorithmic approaches (within the program RiSC by the KIT and the State of Baden-Württemberg)
- An algorithm for finding the Veech group of an origami. Experimental Mathematics 13, No.4, 459-472 (2004) (final version in Experimentals).
- 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. Journal of Modern Dynamics (JMD) 4, No.4, 715 - 732 (2010).
- Veech groups of Loch Ness monsters. Together with Piotr Przytycki and Ferran Valdez. Ann. Inst. Fourier 61, No.2, 673 - 687 (2011).
- On the geometry and arithmetic of infinite translation surfaces. Together with Ferran Valdez. Preprint arXiv:1102.0974v1.
- Explicit Teichmüller curves with complemetary series. Together with Carlos Matheus. To appear in Bulletin de la Société Mathématique de France.
- The deficiency of being a congruence group for Veech groups of origamis. Accepted in International Mathematics Research Notices, arXiv:1208.1936v1
- Some examples of isotropic SL(2,R)-invariant subbundles of the Hodge bundle. International Mathematics Research Notices 2014; doi: 10.1093/imrn/rnu207
- Finite translation surfaces with maximal number of translations. Together with Jan-Christoph Schlage-Puchta. Preprint arXiv:1311.7446 math.GT
- Christmas-Workshops in Geometry and Number Theory
- International Conference and Workshop on surfaces of infinite type, July 29th - August 2nd 2013 in Morelia (Mexiko)
- Conference Geometry, Groups and Topology 2013, October 7th - 11th in Karlsruhe
Teaching in former terms
|Winter 2008/2009||Seminar Homological algebra|
|Summer 2008||Seminar The Veech alternative for billiard tables|
|Winter 2007/08||Geometric group theory|
|Proseminar "Nice groups of Matrices"|
|Summer 2006||Seminar "Automatic groups"|
|Summer 2005||Seminar "Hodge-Theory"|
|Winter 2004/05||Seminar "Tertium datur: Thurston's classification of surface diffeomorphisms"|
|Summer 2003||Seminar "Moduli spaces of algebraic curves"|
|Winter 2002/03||Exercise Sections for Algebra I|
|Seminar "Fuchsian groups"|
|Summer 2002||Proseminar "Geometry and Combinatorics"|
|Winter 2001/02||Proseminar "Knot-Theory"|