This conference focus on applications of non-positive and negative curvature to geometric group theory. The most well known examples of this are δ-hyperbolic and CAT(0)-groups. More recently, some of the techniques that have been used to study these groups have been imported to study groups that have some features of negative curvature but aren’t themselves negatively curved. For example, the mapping class group is neither δ-hyperbolic nor CAT(0) but major progress has been obtained in on our understanding of this group by studying its action on the δ-hyperbolic curve complex. A related group is Out(Fn), the group of automorphisms of the rank n free group and similar program is underway to understand it. More generally, large classes of groups have been identified that have certain features of negative curvature and this has been exploited to prove results which were heretofore only known in special cases. This conference bring together a distinguished international group of mathematicians to report on current work and to explore future directions in this active and expanding area of research.