The Forbidden Number

Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is a new invariant we call the forbidden number. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots. This is joint work with Sandy Ganzell and Blake Mellor.