Archimedean Closure and Property FD

In this talk, I will introduce the concept of Archimedean closedness - a concept from real non-commutative algebraic geometry which determines when "positivity" of an element (captured through *-representations) in a *-algebra can be completely certified algebraically. On the other hand, property FD is a representation theoretic property of groups depicting when any representation of a group can be approximated by finite representations in the unitary dual. I will try to connect these two seemingly very different concepts through some examples and speculations. This is a work in progress.