Amazingly, splines are not just of practical interest in applications, but also are interesting from a purely theoretical mathematical perspective. This workshop brings together researchers from different mathematical communities: on the applied side, those working in numerical analysis and approximation theory, and on the theoretical side, those working in GKM theory, equivariant cohomology and homological algebra. The aim is to bring theory and practice together, and to build collaborations between researchers from different areas. The advancement of knowledge often arises from integration of seemingly different fields.