Geometry, Topology and Dynamics Seminar
Jason DeBlois
UIC/Stanford/Pittsburgh
Points on hyperbolic surfaces
Abstract: A finite subset S of a closed, orientable hyperbolic surface F canonically determines an embedded graph on F,
something like a Delaunay triangulation, with geodesic edges and vertex set S. I will define this graph and describe
some of its geometric properties. The goal is to produce a machine that can rule out the following kinds of situations:
all geodesic arcs on F with endpoints in S are "very long"; or there are few "short" arcs with endpoints in S and all
other such arcs are "much longer". I will give results that in specific cases attach sharp constants to the phrases in
quotes above.
Monday September 13, 2010 at 3:00 PM in SEO 612