Title: 
Sublinear rigidity of lattices in semisimple Lie groups. 

Abstract: 
Sublinear Bilipschitz Equivalence (SBE) is a weak form of quasi-isometry, in which the additive constant is replaced by a function which grows sublinearly in the distance to a fixed base point. I will present results of 'SBE-rigidity' of lattices in semisimple Lie groups, generalizing the quasi-isometric rigidity of these lattices. I will present the proof for Q-rank 1 lattices, which is mostly geometric and consists of proving the existence of a horospherical lattice.