  This work establishes a deep connection between two seemingly distant
branches of nuclear physics: nuclear structure and relativistic heavy-ion
collisions. At the heart of this connection is the recent discovery made at
particle colliders that the elliptic flow of outgoing hadrons in central
nucleus-nucleus collisions is strongly impacted by the quadrupole deformation
of the colliding nuclear species. I review the physics of the soft sector of
relativistic heavy-ion collisions, and I explain that the interpretation of
elliptic flow data in central $^{197}$Au+$^{197}$Au, $^{238}$U+$^{238}$U, and
$^{129}$Xe+$^{129}$Xe collisions requires a deep understanding the structure of
these ions. Subsequently, I introduce a technique that permits one to isolate
collision configurations in which the deformed shapes of the colliding nuclei
maximally break rotational (azimuthal) symmetry in the interaction region. This
allows me to construct observables that possess an unparalleled sensitivity to
the quadrupole deformation of the colliding ions, and thus to conclude that
nuclear experiments at high energy can be used to place new quantitative
constraints on the deformation of atomic nuclei. I emphasize the great
opportunities offered by potential collider experiments aimed at the systematic
study of nuclear deformation across the valley of stability.
