This (by invitation only) meeting gathers together researchers from three different communities: approximation theorists, workers in GKM theory and group actions, and algebraic geometers. They have all encountered -sometimes unknowingly- multivariate splines, and the workshop's aim is to foster collaborations among them in a beautiful setting such as the Palazzone di Cortona (Arezzo, Italy).

Conference topics include:

• Bernstein-Bézier techniques

• Homological techniques for investigating spline properties

• Dimension of spline spaces on triangular, tetrahedral and polyhedral partitions

• Extension of multivariate polynomial splines

• Splines in representation theory and topology via GKM-theory.

• Schubert calculus for spline investigation