Abstract: Let F be a finitely generated (f.g.) nonabelian free group. O. Kharlampovich and A. Myasnikov proved that any f.g. group H containing a distinguished copy of F (H is called an F -group in the algebraic geometry over groups) is universally equivalent to F ( i.e., satisfies precisely the same universal sentences as F does in a first order language appropriate for group theory where all the elements of F are taken as constants - called the language of F ) if and only if there is an embedding of H into a Lyndon's free exponential group, F_Z[t] , which is the identity on F (this is called an F -embedding in the algebraic geometry over groups). Alexei Myasnikov then posed the question as to whether or not a similar result holds for f.g. free nilpotent groups with Lyndon's group replaced with Philip Hall's completion with respect to a suitable binomial ring. We (Dennis Spellman and myself ) answered Alexei's question in the affirmative. This talk will explain our answer.