Title: Taut foliations of compact 3-manifolds with constrained boundary slopes

Abstract: A codimension one foliation of a 3-manifold is called taut if there exists a simple closed curve in the manifold that intersects each leaf of the foliation transversally. A surface bundle over a circle is a simple example of a 3-manifold with a taut foliation. Every compact 3-manifold can be obtained from such a surface bundle by Dehn filling the boundary components, i.e., by sticking a solid tori to the torus boundaries. We have proved that the fiber structure of a surface bundle (with possibly disconnected boundary) can be perturbed to taut foliations that realise all rational boundary slopes in a neighbourhood of the the boundary slopes the fiber. This is joint work with Rachel Roberts.