MATHEMATICS COLLOQUIUM
Speaker: Peter Buser
Title: Graphical Presentation of the Birman-Series
Set on Hyperbolic Surfaces
Affiliation: Swiss Federal institute of Technology
Date: Friday, January 9, 2009
Place and Time: Room 101, Love Building, 3:35-4:30 pm
Refreshments: Room 204, Love Building, 3:00 pm
Abstract.
It is well known that complete geodesics on a compact negatively
curved manifold are dense. In contrast to this, Birman
and Series showed that in dimension two (and constant curvature),
the sublocus of this set formed by the simple complete geodesics
is nowhere dense. The lecture presents algorithms that compute
this set up to a given degree of accuracy. A difficulty occurs
from the fact that in negative curvature, geodesics spread with
exponential speed. In the lecture it is shown how one may solve
this without having to resort to ultra high precision.
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