Right angled cocompact lattices in higher rank simple Lie groups.
Let G be a simple Lie group of real rank at least 2 and let L be a lattice in G. When G/L is not compact then L is known to have fixed price 1 and rank gradient zero. The main purpose of this talk is to give examples of cocompact lattices with the same property. This is joint work with M. Abert and T. Gelander.