Quantum Gravity Phenomenology… Done carefully

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In this talk I will discuss issues and possibilities to outline Quantum Gravity Phenomenology using cosmological and astrophysical data. After a brief review on some formal aspect of the problem I will focus on the analysis of in-vacuo dispersion features for GRB (gamma-ray-burst) neutrinos of energy in the range of 100 TeV, and for GRB photons with energy in the range of 10 GeV. I will introduce a strategy of data analysis which has the advantage of being applicable to several alternative possibilities for the laws of propagation of neutrinos and other particles in a quantum spacetime. Far from being conclusive, the results to be shown should nonetheless motivate a vigorous program of investigation following the methodology of multi-messenger astronomy.