As shown by Dani, diophantine approximations are in direct correspondence to the behavior of orbits in certain homogeneous spaces. We will discuss the interpretation of the divergent trajectories and the obvious ones, the ones diverging due to a purely algebraic reason. As conjectured by Weiss, there is a complete classification of divergent trajectories when considering the action of subgroups of the diagonal group. We will discuss the last part of this conjecture, showing that for a 'large enough' such subgroup, every divergent trajectory diverges obviously. This is a joint work with Omri Solan.
Speaker(s): Nattalie Tamam (U Michigan)