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

Complex hyperbolic lattices occupy an interesting space in between fundamental groups of hyperbolic manifolds and higher-rank lattices, and they also are a key case for a number of open problems on discrete subgroups of Lie groups. This mini-course will discuss (0) basic geometry (1) rigidity and a geometric viewpoint on arithmeticity (2) explicit constructions via uniformization and applications and (3) a potpourri of open problems.