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Workgroup on Number Theory and Algebraic Geometry

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 1.027

Address
Englerstraße 2, 76131 Karlsruhe

Office hours:
Mo - Fr, 9.15 - 11.45

Tel.: +49 721 608 43041

Fax.: +49 721 608 44244

Photo of André Kappes Dr. André Kappes

Office hour for students: Wann immer ich da bin.
Room: 1.036 Kollegiengebäude Mathematik (20.30)
Tel.: 0721 608 4 2706
Fax.: 0721 608 4 4244
Email: andre.kappes@kit.edu

Karlsruher Institut für Technologie (KIT)
Fakultät für Mathematik
Institut für Algebra und Geometrie
Kaiserstraße 89-93
76133 Karlsruhe

Since October 1, I am at the Goethe-Universität Frankfurt/Main.





Semester Titel Typ
Summer Semester 2011


Research

Origamis are translation surfaces obtained by gluing finitely many unit squares. These combinatorial objects provide an easy access to Teichmüller curves - algebraic curves in the moduli space of curves. In particular, their monodromy represenation, the action of the fundamental group of the Teichmüller curve on the cohomology of the fibre, can be explicitely determined. In my Ph.D. thesis, a general principle for the decomposition of this represenation is exhibited and then applied to examples. Closely connected to it is a dynamical cocycle, the Kontsevich-Zorich cocycle on the Teichmüller curve. By the work of M. Kontsevich, the Lyapunov exponents that govern the dynamics of the cocycle are related to degrees of certain line bundles on the Teichmüller curve. Using this relationship, it is shown that the Lyapunov exponents, otherwise inaccessible, can be computed in the case of a subrepresentation of rank two.

You will find more on origamis on the webpage origamis in Karlsruhe.

Publications/Preprints

  • A. Kappes, On the Equation of an Origami of Genus two with two Cusps, Diploma thesis, (last changes: April 10, 2007) (.pdf-file)
  • F. Herrlich, A. Kappes, G. Schmithüsen, An origami of genus 2 with a translation, preprint (2008) (.pdf-file)
  • A. Kappes, Monodromy Representations and Lyapunov Exponents of Origamis, Ph.D. thesis, May 2011 (.pdf-Datei)