Sublinear Rigidity of Lattices in Semisimple Lie Groups

I will talk about the coarse geometry of lattices in real semisimple Lie groups. One great result from the 1990’s is the quasi-isometric rigidity of these lattices: any group that is quasi-isometric to such a lattice must be, up to some minor adjustments, isomorphic to lattice in the same Lie group. In this talk I present a partial generalization of this result to the setting of Sublinear Bilipschitz Equivalences (SBE): these are maps that generalize quasi-isometries in some `sublinear’ fashion.