  Neutrinos can push our search for new physics to a whole new level. What
makes them so hard to be detected, what allows them to travel humongous
distances without being stopped or deflected allows to amplify Planck
suppressed effects (or effects of comparable size) to the level we can measure
or bound in DUNE. In this work we analyse the sensitivity of DUNE to CPT and
Lorentz--violating interactions in a framework that allows a straightforward
extrapolation of the bounds obtained to any phenomenological modification of
the dispersion relation of neutrinos.
