Seminars & Colloquia Calendar

Abstract: The celebrated Ratner's orbit closure theorem proved around 1990 says that in a homogeneous space of finite volume, the closure of an orbit of any subgroup generated by unipotent flows is homogeneous. A special case of Ratner’s theorem (also proved by Shah independently) implies that the closure of a geodesic plane in a hyperbolic manifold of finite volume is always a properly immersed submanifold. Searching for analogs of Ratner's theorem in the infinite volume setting is a major challenge. We present a continuous family of hyperbolic 3-manifolds, and a countable family of higher dimensional hyperbolic manifolds of infinite volume, for which we have an analogue of Ratner’s theorem.

(Based on joint work with McMullen, Mohammadi, Benoist and Lee in different parts.)