Laminations on the Circle and Hyperbolic Geometry

We will see that laminations can be used to study groups acting
on the circle. In particular, it is possible to characterize Fuchsian
groups in terms of topological invariant laminations. It is a
geometrization result in the sense that you start with a topological
dynamical data and hyperbolic geometry comes out of the picture.
Main motivation of this program is Thurston's universal circle theory for
tautly foliated 3-manifolds. We will also discuss how this program is
connected to Cannon's conjecture if time permits.