Title: Colored Tri-Plane Diagrams and the Slice-Ribbon Problem

Abstract: We study dihedral branched covers of the four-dimensional sphere, where the branching set is a surface with one singularity modeled on the cone on a knot K.   We construct examples of these covers using colored tri-plane diagrams, which are triples of tangles that can be used to describe a surface in the four-sphere.  We also show that a knot invariant arises in this context, which can potentially be used to prove that a slice knot is not ribbon.