Space-Time from the spectral point of view

Abstract: We develop the spectral point of view on geometry based on the formalism of quantum physics. We start from the simple physical question of specifying our position in space and explain how the spectral geometric point of view provides a new paradigm to model space-time whose fine structure can be encoded by a finite geometry. The classification of the irreducible finite geometries of KO-dimension 6 singles out a ``symplectic--unitary" candidate F, which when used as the fine texture of space-time delivers from pure gravity on M x F the Standard Model coupled to gravity and, once extrapolated to unification scale, gives testable predictions.