The course will focus on the theory of lattices and random subgroups. We will cover the following topics:
1. Basic notions in the theory of lattices.
2. Arithmetic groups.
3. Borel--Harish-Chandra theorem.
5. Invariant Random Subgroups.
6. The results of the 7 samurais.
7. Stationary Random Subgroups.
8. Manifolds of infinite volume.