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We present a new framework for defining fuzzy approximations to geometry interms of a cutoff on the spectrum of the Dirac operator, and a generalizationof it that we call the Dirac-Flux operator. This framework does not require asymplectic form on the manifold, and is completely rotation invariant on anarbitrary n-sphere. The framework is motivated by the formalism of HolographicSpace-Time (HST), whose fundamental variables are sections of the spinor bundleover a compact Euclidean manifold. The strong holographic principle (SHP)requires the space of these sections to be finite dimensional. We discussapplications of fuzzy spinor geometry to HST and to Matrix Theory.

Fuzzy Geometry via the Spinor Bundle, with Applications to Holographic Space-time and Matrix Theory