On the structure and arithmeticity of lattice envelopes
  We announce results about the structure and arithmeticity of all possible lattice embeddings of a class of countable groups which encompasses all linear groups with simple Zariski closure, all groups with non-vanishing first l2-Betti number, word hyperbolic groups, and, more general, convergence groups. 
Uri Bader and Alex Furman and Roman Sauer
math.GR