GRAPES aims at significantly advancing the state of the art in a variety of fields ranging from Computational and Numerical Mathematics, to Geometric Modelling and CAD, up to Data Science and Machine Learning, in order to promote game changing approaches for generating, optimising, and learning 3D shapes. Research is articulated around 3 scientific work packages: 1. High-order methods and representations 2. Algebraic & numeric tools in shape optimisation and analysis 3. Machine Learning for shapes Concrete applications include simulation and fabrication, design and visualisation, manufacturing and 3D printing, retrieval and mining, reconstruction and urban planning. Our 15 PhD candidates shall benefit from both top-notch research as well as a strong innovation component through a nexus of intersectoral secondments and Network-wide workshops. Ιnnovation and technology transfer is supported by the active participation of SMEs, either as beneficiary, or as associate partners hosting secondments