Geometro-kinematics and dynamics in a discrete setting

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A quantum theory of gravity implies a quantum theory of geometries. To
this end we will introduce different phases spaces and choices for the
space of discretized geometries. These are derived through a canonical
analysis of simplicity constraints - which are central for spin foam
models - and gluing constraints. We will discuss implications for
spin foam models and map out how to obtain a path integral
quantization starting from a canonical quantization.