On the sublinear classification and rigidity of lattices in semisimple Lie groups

Sublinear Bilipschitz Equivalence (SBE) is a weak form of quasi-isometry, originally brought forward and used by Cornulier in studying the geometry of solvable Lie groups. In contrast with solvable Lie groups, the SBE-class of a semisimple Lie group of noncompact type is the same as its isometry class. I will present this SBE-classification, and then focus on the situation for non-uniform lattices: what is known and what is still open. 

Based on joint work with Gabriel Pallier (Lille).