Georgia Institute of Technology College of Sciences

Giroux and Pardon conjectured that a Lagrangian L in a Weinstein manifold W is regular (that is, compatible with the Weinstein structure in a natural sense) if there is a Lefschetz fibration p: W \to \C such that p(L) is a ray. In this talk, I will discuss forthcoming joint work with A. Roy and L. Wang, which establishes this conjecture. As an application of the proof, we show how all fillings of the rainbow closures of a positive braid can be described by manipulations of arcs in the base of an appropriate Lefschetz fibration.