The subject of 3-manifold topology has a long history of deep and interesting interactions with other parts of mathematics. The complexity of these connections has increased with time, as the subject developed, and has exploded in recent years. The coincidence of this explosion with the recent solution of several of the major outstanding problems in the area make this a good time for reflection on its relationship to the rest of mathematics. This conference aims to bring together a varied group of leading researchers whose work demonstrates deep connections between 3-manifold topology and other areas of mathematics. The areas covered include: geometrization of 3-manifolds; combinatorial group theory and coarse geometric properties of groups; properties of random 3-manifolds and asymptotic properties of hyperbolic surfaces; Floer homology, Khovanov-Rozansky homology; 3-manifold invariants arising from contact structures; character varieties; and Dehn surgery. The conference will honor Peter Shalen, whose work has been a major force in bringing many different aspect of mathematics to bear on the study of 3-manifolds, and in expanding the influence of 3-manifold topology into other areas.