Abstract: In this talk, we will discuss an effective disjointnesstheorem of trivial and ergodic systems on homogeneous spaces. This has a
variety of surprisingly strong applications, one of which is towards
effective equidistribution of rational subspaces and their shapes
following Maass, Schmidt and many others. If time remains, we will also
discuss applications to complex multiplication points on the modular
curve. The talk is based on joint work with Menny Aka, Manfred
Einsiedler, Manuel Luethi, and Philippe Michel.