Bonahon will study the classification problem for Kleinian groups. As a first step, he plans to investigate the topological type of the limit set of a Kleinian group. In a different but closely related domain, he wants to study the geometry of the Teichmuller space of a surface from the viewpoint of geodesic currents, which he has developed in some of his earlier work. These are classical problems of geometric analysis attacked by topological means. The methods developed will be widely appreciated in mathematics and neighboring disciplines.
