Geometry, Topology and Dynamics Seminar
Patrick Hooper
Northwestern
Grid graphs and the lattice property
Abstract: A translation surface is a finite collection of polygonal subsets of
the plane with edges identified in pairs by translations. There is an
action on the space of translation surfaces by SL(2,R). The subgroup
of SL(2,R) which `fixes' a surface S is known as the Veech group of S.
Veech showed that this group must be discrete, and if this group is a
lattice then the geodesic flow on the surface has many nice dynamical
properties.
In 2006, Bouw and Moeller produced translation surfaces which realize
nearly every triangle group as a Veech group. I will describe an
elementary construction of many of their surfaces. These surfaces turn
out to arise from eigenvectors of grid graphs (rectangular subgraphs
of the square tiling of the plane).
Monday December 1, 2008 at 3:00 PM in SEO 612