Some of the most important goals of our Collaboration include:

• Construct an array of new special holonomy spaces, especially those with singularities compatible with realistic physical models in M-theory, e.g. compact singular Calabi–Yau and exceptional holonomy spaces with isolated conical singularities; collapsing families of exceptional holonomy spaces; new local models for singularities of exceptional holonomy spaces.
• Understand the physical predictions for the geometry of special holonomy spaces and conversely understand the physics of new special holonomy spaces and their associated geometric structures.
• Develop analytic and geometric foundations for potential enumerative theories “counting” higher dimensional instantons and calibrated submanifolds; understand the fundamental nature of the structure encoded by such a theory.