I will report on joint work with O. Becker and P. Varju, in which we study the G-representation variety and G-character variety of a typical finitely presentation group with values in a semi simple algebraic group. We can in particular determine their dimension, Galois action on components, and obtain lower bounds on Galois orbits, yielding many examples of Galois-generic rigid Zariski-dense subgroups of G. The proofs make key use of mixing bounds via the classification of approximate subgroups of finite simple groups of Lie type and only work under GRH.