Description:

Title: Horocycles in geometrically finite rigid acylindrical manifolds

Abstract: The Ratner-Shah theorem states that the closure of a horocycle in a finite-volume hyperbolic 3-manifold is always a properly immersed submanifold. Classifying horocyclic orbit closures beyond the classical setting remains an important problem. Following the pioneering work of McMullen-Mohammadi-Oh on generalizing the Ratner-Shah theorem to infinite-volume manifolds, there have been many exciting developments. In this talk, I will present joint work with Dongryul Kim, in which we classify horocyclic orbit closures for a class of geometrically finite 3-manifolds and discuss how our results fit into the broader literature.