Explaining gravitational-wave (GW) observations of binary neutron star (BNS) mergers requires
an understanding of matter beyond nuclear saturation density. Our current knowledge of the
properties of high-density matter relies on electromagnetic and GW observations, nuclear physics
experiments, and general relativistic numerical simulations. Using a phenomenological nonconvex
equation of state (EoS) we conduct a suite of numerical-relativity simulations of BNS mergers
and identify observable imprints on the GW spectra of the remnant. Nonconvex regions may
be associated with first order phase transitions from nuclear/hadronic matter to deconfined quark
matter, present in some realistic EoS from nuclear physics. The dynamics triggered by our
nonconvex EoS induces a significant shift in the peak frequency of the dominant oscillation mode
of the post-merger remnant (of order $\Delta f \gtrsim 380$ Hz) with respect to that of binaries with convex
(or regular) dynamics.