Abstract: The slice-ribbon conjecture states that a knot in the three
sphere is the boundary of an embedded disc in the four ball if and only if
it bounds a disc in the sphere which has only ribbon singularities. This
conjecture was proposed by Fox in the early 70s. There doesn't seem to be
any conceptual reason for it to be true, but large families of knots (i.e.
pretzel knots, two bridge knots) satisfy it. In this seminar we will prove
that the conjecture remains valid for a large family of Montesinos knots.
The proof is based on Donaldson's diagonalization theorem for definite four
manifolds.