The theory of Kleinian groups is many faceted and in turn uses ideas from many other subjects. Haas' previous work has been a good example of this. He has studied Diophantine problems and has successfully used ideas from Riemann surfaces in his work with Series on the Lagrange spectrum of the Hecke groups. In the current project Haas will continue to focus on Kleinian groups and the geometry of their associated Riemann surfaces and 3-manifolds. Diophantine problems will be investigated from a hyperbolic geometric point of view, the problem of elliptic elements in Kleinian groups will be pursued jointly with Abikoff and aspects of the geometry and topology of geometrically infinite Kleinian groups will be studied.
