Conformal and Noncommutative Gravity from Gauge Symmetry Breaking and SO(2,16) Unification

Motivated by the old idea of treating gravity as a gauge theory, we review the gauge-theoretic construction of Conformal Gravity and of Noncommutative (Fuzzy) Gravity. We then outline how these gauge formulations of gravity can be unified with internal interactions described by an SO(10) Grand Unified Theory, based on the critical observation that the dimension of the tangent-space symmetry group of a curved manifold need not coincide with the spacetime dimension.