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Dynamics Seminar
February 3, 2009

Andres Kappas
University of Chicago

Teichmüller curves from origamis

An origami, also called square-tiled surface, arises from gluing finitely many squares along their edges by translations. These combinatorial objects are interesting in many aspects and studied e.g. in dynamical systems, algebraic geometry and number theory.
In particular, origamis provide a means to obtain Teichmüller curves in the moduli space of Riemann surfaces, i.e. algebraic curves that are isometrically immersed for the Teichmüller metric.
In genus 2, Teichmüller curves have been almost completely classified by C. McMullen. I will talk about an attempt to complete the remaining classification of Teichmüller curves in the stratum H(1,1) arising from origamis.

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