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A review of Spinfoams and Group Field Theory

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We will review the definitions of spin foam models for quantum gravity and the recent advances in this field, such as the "graviton propagator", the definition of coherent states of geometry and the derivation of non-commutative field theories as describing the effective dynamics of matter coupled to quantum gravity. I will insist on the role of group field theories as providing a non-perturbative definition of spinfoams and their intricate relation with non-commutative geometry and matrix models.