The behaviour of gravitation in the quantum regime is one of the most
important pieces still missing in our understanding of the universe. Beyond
the plethora of unsuccessful attempts to build a consistent theory for
Quantum Gravity, intuition points to the possible existence of a quantum
structure of space-time that could manifest itself as an energy dependence
of the speed of light in vacuum. In this seminar the present bounds coming
from time-of-flight measurements from distant astrophysical sources will be
summarized and the technique used will be scrutinized. Also the impact of
the recent neutron start merger event detected in both, Gravitational and
Electromagnetic waves, will be commented.
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