Lattices, superrigidity and surfaces

One of the most well known open questions in geometric group
theory is the following question of Gromov: is it true, that every one-ended hyperbolic group
contains a surfaces group? Even if we restrict ourselves to groups acting
on hyperbolic buildings the answer is not known in general. We'll present some non-obvious
embeddings of surfaces groups into groups acting on buildings as well as some
negative results, leaving a possibility for counter-examples.