Seminar

Corlette and Gromov--Schoen established analogues of Margulis superrigidity theorem for lattices in the isometry group of the n-quaternionic hyperbolic space, n>1, and the isometry group of the octonionic hyperbolic plane. In this talk, I will survey some constructions of finitely presented groups with restricted linearity and discreteness properties, obtained from superrigid  hyperbolic lattices. These include constructions of nonlinear hyperbolic groups, hyperbolic groups indiscrete in rank 1 and robustly discrete hyperbolic subgroups of SL(n,C) which fail to be Anosov.