Title: Spinal open book decompositions and symplectic fillings

Abstract: Recently, C. Wendl used holomorphic curves to show that any strong filling of a planar open book comes as an extension of the open book to a Lefschetz fibration of the filling. I'll discuss a generalization of this result to spinal open books and discuss some applications, including the classification of symplectic fillings of the lens spaces L(p,1) and a determination of fillability for contact structures on circle bundles. Part of this is joint with O. Plamenevskaya and part of this is joint with S. Lisi and C. Wendl.