Planck-scale-deformed relativistic symmetries and applications in astrophysics

This thesis research work has been mainly devoted to addressing the possibility that we might be observing some GRB neutrinos affected by in-vacuo dispersion; moreover, for GRB photons, the abundance of observations cumulatively obtained by the Fermi telescope reached a level sufficient to allow us to perform a statistical analysis over the whole collection of observed GRBs. The outline of the thesis will be the following: the first part is directed to a mathematical overview of relativistic symmetries and their representations, starting from Galilean relativity to Planck-scale-deformed special relativity, while the other parts of the thesis, after introducing the physics of GRBs and high-energy neutrinos, will concern the phenomenological results for both neutrinos and photons from GRBs, as well as the quantification of their statistical significance.