|Dept.||TATA tata institute of fundamental research|
I will give an introduction to the distribution of discrete and dense lattice orbits on homogeneous spaces. An elementary example is the linear action of SL(2, Z) on the plane. Even for such a simple action, there are many interesting difficult open questions. If time permits, I will present some recent progress. The latter is joint work with A. Gorodnik and A. Nevo.