Loop Quantum Gravity on lattice: toward effective dynamics

A derivation of the classical limit of LQG -- leading to the emergence of GR -- is still missing. In this talk, I will consider a family of LQG coherent states that represent discrete spatial geometries. I will investigate the quantum time-evolution of one such state, and discuss that it can be approximated by an effective time-evolution of the corresponding spatial geometry. In this sense, a discrete spacetime geometry emerges dynamically within LQG. Finally, I will discuss some examples: isotropic and anisotropic (Bianchi I) cosmologies; interior of a spherical black hole; gravitational waves on Minkowski background.