Classification of divergent trajectories

The study of group actions and more specifically the behaviour of orbits can be utilized to study Diophantine approximations. We will see the dynamical equivalent to vectors with ‘infinitely good’ diophantine approximations. From this dynamical point of view, Weiss conjectured a complete classification of the relevant trajectories. We will discuss the steps and different tools used in proving the last piece of the conjecture. This is a joint work with Omri Solan.