I will construct singular fibrations on 3–manifolds with boundary, and discuss when they may trace smooth fibrations (over S1) of a 4–manifold X4 with boundary, with particular emphasis on when X4 is the complement of a ribbon disk in B4 whose boundary is a fibered knot in S3. This is related to a question of Casson and Gordon.
(I will define fibered/ribbon knots and singular fibrations, and show how one might visualize a 4–dimensional manifold. This talk will be very heavy on visualization/geometric construction, but not super technical.)