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Dynamics Seminar
January 13, 2009

Joshua Bowman
Cornell University

Flat surfaces, Teichmüller disks, and hyperbolic tessellations

Flat surfaces are locally isometric to the Euclidean plane except at a discrete set of points, each of which has a cone angle that is a multiple of $\pi$. Despite (or perhaps because of) the simplicity of their construction, the study of flat surfaces has applications to a variety of areas of mathematics. For many of these applications, it is important to understand to orbit of a flat surface under a natural group of affine deformations. We will consider a hyperbolic tessellation (also studied by Veech) connected with such an orbit and give some indications of what kinds of information can be extracted from the tessellation.

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