Abstract. For n>1, a generic n--tuple of elements in a connected compact non-abelian Lie group G generates a free group. Margulis and Soifer conjectured that every such tuple can be slightly deformed to one which generates a group which is not virtually free. I will explain a proof of this conjecture, and actually show that for n>2 and for an arbitrary dense subgroup D, with some restriction on the minimal size of a generating set, the set of deformations of F_n whose image is D is dense in the variety of all deformations. The proof relies on the product replacement method. Using the same ideas I will also give a proof of a conjecture of Goldman on the ergodicity of the action of Out(F_n) on Hom(F_n,G)/G when n>3. For n=2, I will explain how to produce for any pair (a,b) an arbitrarily close pair (a',b') which generates an infinite group which has Serre property FA and in particular is not virtually free.