Quantum Chromodynamics (QCD) is the fundamental theory of strong interactions. The medium described by QCD is known to undergo various phase transitions under extreme conditions of high temperature or high baryon density, such as those realized in the early Universe and in the cores of neutron stars. These transitions, including quark deconfinement and chiral symmetry restoration, have been extensively studied over the past decades using theoretical, experimental, and numerical approaches. In this lecture, I will provide an overview of these topics, with particular emphasis on recent progress in lattice QCD numerical simulations and experimental studies in relativistic heavy-ion collisions. The lecture will range from basic concepts to the latest developments in the field.

Neutron stars provide a unique laboratory in which nuclear physics and astrophysics are intimately connected. Their extreme densities, reaching several times that of normal nuclear matter, allow us to explore properties of strongly interacting matter far beyond the reach of terrestrial experiments. At the same time, precise astrophysical observations, such as the mass–radius measurements of pulsars by NICER and the tidal deformability extracted from gravitational-wave events, offer stringent constraints on the nuclear equation of state (EoS). Bridging these perspectives has become one of the central challenges in modern hadron and nuclear physics. From the nuclear side, the symmetry energy plays a crucial role in determining the properties of isospin-asymmetric nuclear EoSs. While laboratory experiments provide valuable input, large uncertainties remain at supra-saturation densities. From the hadronic side, the composition of dense matter may include hyperons or even quark matter at very high densities. These additional degrees of freedom tend to soften the nuclear EoS and threaten the stability of the two-solar-mass neutron stars that have been observed, leading to the so-called hyperon puzzle. In this seminar, I will present recent progress using relativistic mean-field models and an SU(3) flavor-symmetric treatment of vector-meson couplings. These improvements allow hyperons to appear consistently with nuclear data while maintaining sufficiently stiff EoSs to explain massive neutron stars. I will also discuss our recent studies of quarkyonic (quark+baryonic) matter within the quark–meson coupling model, which provide a dual description of baryons and quarks and explore how dense matter may evolve smoothly from hadronic to quark degrees of freedom. Such approaches may offer new insights into the nature of strongly interacting matter while helping to build a unified picture of neutron stars.

Born from gravitational-core collapse supernovae, with initial temperatures as high as ~10^12K, neutron stars cool down to temperatures 10^9K within a few days, providing a unique opportunity to explore matter under extreme conditions. In particular, neutron stars contain nuclear superfluids whose presence is supported by observations of pulsar frequency glitches, rapid decline in luminosity of the Cassiopeia A remnant, and crust cooling of neutron stars in low-mass X-ray binaries. Despite the importance of the superfluid dynamics in interpreting these astrophysical phenomena, most microscopic calculations of the nuclear pairing properties have been carried out so far for static situations. We have recently studied the dynamics of hot neutron-proton superfluid mixtures within the time-dependent nuclear energy-density functional theory. The disappearance of superfluidity has also been investigated and reveals the presence of a dynamical "gapless" state in which nuclear superfluidity is not destroyed even though the energy spectrum of quasiparticle excitations exhibits no gap. The absence of an energy gap affects considerably the neutron specific heat which becomes very different from that in the classical BCS state (in the absence of superflows). Implications for the crust cooling of neutron stars in low-mass X-ray binaries will be discussed, as well as the consequences of gapless superfluidity for neutron vortex dynamics.

Chiral symmetry is a fundamental symmetry of hadrons. One of the important properties of chiral symmetry is provided by the existence of chiral doublets (pairs of hadrons with positive and negative parities). The degeneracy of the two hadrons in a chiral doublet can be realized at high densities inside the neutron star due to the chiral symmetry restoration. In this talk, we focus on nucleons and N*(1535) as the baryons in the chiral doublet, and discuss superfluids due to the interaction between nucleons and N*(1535) at high densities. We propose the emergent chiral symmetry as a generalized symmetry including both naive and mirror representations in the chiral doublet, and adopt Z2 symmetry or SU(2) symmetry as internal symmetries. Under these symmetries, we consider the gap equation for the four-point interaction between nucleons and N*(1535), and obtain the phase diagram of superfluidity. We show that there exist gapless fermions and topological structures in the superfluid and they can provide a new view on the internal structure of neutron stars.

Understanding the dynamics of hadrons with strangeness has received a lot attention over the past decades in connection with the study of exotic atoms, the analysis of strangeness production and propagation in particle and nuclear research facilities, and the investigation of the possible strange phases in the interior of neutron stars. One venue of interest in the field of strangeness is the study of strange baryons, the so-called hyperons. In this talk I will review the dynamics of hyperons with nucleons and nuclear matter. I will also discuss the presence of hyperons in the inner core of neutron stars as well as the consequences for the structure of these compact stars and their dynamics in neutron starmergers.