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Lattice QCD (LQCD) calculations predict that chiral symmetry is restored in a smooth crossover transition between a quark-gluon plasma and a hadron resonance gas (HRG) at vanishing net-baryon density, a condition realized in heavy-ion…

I review recent theoretical developments which show how a key qualitative feature of the QCD phase diagram, namely a critical point which in a sense defines the landscape which heavy ion collision experiments are seeking to map, can be…

The QCD topological observables are essential inputs to obtain theoretical predictions about axion phenomenology, which are of utmost importance for current and future experimental searches for this particle. Among them, we focus on the…

For the discovery of the QCD critical point it is crucial to develop dynamical models of the fluctuations of the net-baryon number that can be embedded in simulations of heavy-ion collisions. In this proceeding, we study the dynamical…

The QCD baryon number density can formally be expanded into a Laurent series in fugacity, which is a relativistic generalization of Mayer's cluster expansion. We determine properties of the cluster expansion in a model with a phase…

In this review, I recall the nature and the inevitability of the "sign problem" which plagues attempts to simulate lattice QCD at finite baryon density. I present the main approaches used to circumvent the sign problem at small chemical…

In the context of the ongoing search for the QCD critical point at the Relativistic Heavy-Ion Collider, we study the equation of state near the critical point in the temperature and baryon chemical potential plane. We use the parametric…

Supplementing the holographic Einstein-Maxwell-dilaton model of [O. DeWolfe, S.S. Gubser, C. Rosen, Phys. Rev. D83 (2011) 086005; O. DeWolfe, S.S. Gubser, C. Rosen, Phys. Rev. D84 (2011) 126014] by input of lattice QCD data for 2+1 flavors…

A new approach is presented to explore the singularity structure of lattice QCD in the complex chemical potential plane. Our method can be seen as a combination of the Taylor expansion and analytic continuation approaches. Its novelty lies…

The theory of quantum chromodynamics (QCD) encodes the strong interactions that bind quarks and gluons into nucleons and that bind nucleons into nuclei. Predictive control of QCD would allow nuclear structure and reactions as well as…

We investigate the critical end point of QCD with two flavours of light dynamical quarks at finite lattice cutoff a=1/4T using a Taylor expansion of the baryon number susceptibility. We find a strong volume dependence of the position of the…

The equation of state (EoS) of QCD is a crucial input for the modeling of heavy-ion-collision (HIC) and neutron-star-merger systems. Calculations of the fundamental theory of QCD, which could yield the true EoS, are hindered by the infamous…

The recent net-proton fluctuation results of the STAR (Solenoidal Tracker At RHIC) experiment from beam energy scan (BES) program at the BNL Relativistic Heavy Ion Collider (RHIC) have drawn much attention to exploring the QCD critical…

We study QCD at non-zero quark density, zero temperature, infinite coupling using the Glasgow algorithm. An improved complex zero analysis gives a critical point \mu_c in agreement with that of chiral symmetry restoration computed with…

The baryon-number density formed in relativistic nuclear collisions, versus the chemical potential of the freeze-out states, is systematically studied on the basis of existing measurements. A remarkable power-law behaviour of the…

The study of QCD phase diagram is very interesting, but we have never understood it well. This is because we face a problem at finite density in QCD. The problem is called sign problem. It causes a decrease of the calculation accuracy. This…

We investigate the Taylor expansion of the baryon number susceptibility, and hence, pressure, in a series in the baryon chemical potential (mu_B) through a lattice simulation with light dynamical staggered quarks at a finer lattice cutoff…

Quark number susceptibilities as computed in lattice QCD are commonly believed to provide insights into the microscopic structure of QCD matter, in particular its degrees of freedom. We generalize a previously constructed partonic…

We present a strangeness-neutral equation of state for QCD that exhibits critical behavior and matches lattice QCD results for the Taylor-expanded thermodynamic variables up to fourth-order in $\mu_B/T$. It is compatible with the SMASH…

In the limit of small quark masses, the angle between the temperature axis and the applied magnetic field direction in the three-dimensional Ising model vanishes as $m_q^{2/5}$ when mapped onto the QCD $T-\mu_B$ phase plane. By selecting…