Prof. Gabriela Weitze-Schmithüsen

Prof. G. Weitze-Schmithüsen

Research Interests:

Moduli spaces and deformation spaces of finite and infinite translation surfaces; Veech groups (special subgroups of the mapping class group and (mostly) discrete subgroups of SL(2, R)); Teichmüller curves (special over number fields defined curves in moduli space M_g for projective regular algebraic curves of genus g); origamis (translation surfaces that can be defined by finite graphs); congruence and non congruence groups in SL(2,Z) and generalizations; groups of automorphisms of free groups  and generalizations.

More about my research, including in particular the software on origamis which was written in my working group, can be found on the research page of the working group.

Teaching:

The current and former lectures can be found here.

Note of Lectures:

• Geometric Group Theory (unfinished from Summer 2022)

Some examples of theses:

• Simon Döring (in German): Bestimmung des minimalen Kongruenzlevels für Untergruppen von SL(n,Z) und Sp(n,Z), Bachelor thesis 2021
• Alexander Rogovskyy: Origamis, die zyklisch ueber dem NxN-Torus faktorisieren, Bachelor thesis 2022
• Pascal Schumann: Systoles of Translation Surfaces, Bachelor thesis 2022
• Simon Ertl, Die stabilen Graphen der Randpunkte von Origami-Teichmüllerkurven zu zyklischen Überlagerungen des Torus von Primzahlgrad, Bachelor thesis 2023

Publications:

• 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. Journal of Singularities 9,  2014 (226 -- 244).
• Explicit Teichmüller curves with complemetary series. Together with Carlos Matheus.  Bulletin de la Soci\'et\'e Math\'ematique de France 141, No. 4, 2013 (557 -- 602).
• The deficiency of being a congruence group for Veech groups of origamis. International Mathematics Research Notices, No. 6, 2015 (1613–1637)
• Some examples of isotropic SL(2,R)-invariant subbundles of the Hodge bundle. Together with Carlos Matheus. International Mathematics Research Notices, No. 18, 2015 (8657–8679).
• Finite translation surfaces with maximal number of translations. Together with Jan-Christoph Schlage-Puchta. Israel Journal of Mathematics 217, No. 1, 2017 (1--15).
• Totally non congruence Veech groups. Together with Jan-Christoph Schlage-Puchta. Groups Geom. Dyn. 17, No. 3, 2023 (1115 – 1131).
• Systolic geometry of translation surfaces. Together with Tobias Columbus, Frank Herrlich, Bjoern Muetzel. Experimental Mathematics Published online 2022.
• Arithmeticity of the Kontsevich--Zorich monodromies of certain families of square-tiled surfaces . Together with Etienne Bonnafoux, Manuel Kany, Pascal Kattler, Carlos Matheus, Rogelio Niño, Manuel Sedano-Mendoza, Ferrán Valdez. Preprint arXiv:2206.06595 [math.DS]