Discrete subgroups with full limit sets

In this talk, we'll address the question of whether a discrete subgroup of a higher-rank Lie group G with a full limit set in its Furstenberg boundary must necessarily be a lattice. We'll demonstrate the existence of non-lattice discrete subgroups of G with full limit sets. These groups are infinitely generated, and we'll discuss how they can be constructed using an appropriate sequence of Anosov subgroups. This leaves open the intriguing question of whether finitely generated examples can exist. This is based on joint work with Sebastian Hurtado.