Conjecture, is a result in commutative algebra about the relationship between free modules and projective modules over polynomial rings. It states that every finitely generated projective module over a polynomial ring is free. Certain rings of holomorphic functions arise naturally as classes of transfer functions of stable control systems. Algebraic properties of these rings of transfer functions then play an important role in solving control theoretic problems.
In particular, in this talk we will show an analogue of the Quillen-Suslin Theorem for a particular ring of holomorphic functions and explain the role this plays in the Stabilization Problem in Control Theory.