Title: Fibered knots and open problems in 4D
Abstract: Many seemingly basic questions remain open in 4-dimensional topology: “How many smooth spaces are topologically equivalent to a sphere?" (Poincare conjecture), "How many ways are there to cut a sphere in ‘half’?” (Schoenflies conjecture), "What kinds of surfaces do we expect knots in S^3 to bound in B^4?" (slice-ribbon conjecture).
In this talk, I will discuss these open problems and how they connect to 3-dimensional topology, which we are (usually) better at understanding.