Appears in collection : 2024 - T2 - WS1 - Low dimensional actions

We discuss the question whether a discrete subgroup in a Lie group of higher rank with full limit set in its boundary is necessarily a lattice. We find some necessary conditions for this to be true and discuss some new and old results pointing towards an affirmative answer. Hopefully, we will also relate this discussion to questions about groups acting by diffeomorphisms in low dimensions.

Based on work in progress with Subhadip Dey.