Appears in collection : 2025 - T2 - Higher rank geometric structures

We will consider the problem of calculating the Hausdorff dimension of limit sets of discrete subgroups of SL_2(R) and SL_3(R) with respect to the natural geometric distances on the corresponding spaces of flags. The plan is to begin with basic results on dimension of sets and measures in Euclidean space, including the Moran-Hutchinson theorem. Later discuss the classical techniques and results for SL_2(R) of Bowen, Patterson, and Sullivan. And finally give some idea of what is known for SL_3(R) where active research is still ongoing.