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We discuss several possible caveats which arise with the interpretation of measurements of fluctuations in heavy ion collisions. We especially focus on the ratios of particle yields, which has been advocated as a possible signature of a…

In these two lectures I review the basics of heavy-ion collisions at relativistic energies and the physics we can do with them. I aim to cover the basics on the kinematics and observables in heavy-ion collider experiments, the basics on the…

A summary of discussions on selected topics related to QCD phase diagram, phase transition, critical point, fluctuation and correlations at the Quark Matter 2009 conference are presented.

The evolution of a heavy ion collision passes close to the O(4) critical point of QCD, where fluctuations of the order parameter are expected to be enhanced. Using the appropriate stochastic hydrodynamic equations in mean field near the the…

For the understanding of fluctuation measurements in heavy-ion collisions it is crucial to develop quantitatively reliable dynamical descriptions which take the non-perturbative nature of QCD near the phase transition into account. We…

These lectures start with a brief overview of salient features of the critical region of hot QCD. The main emphasis is on the accurate description of static plasma observables by the well-known hierarchy of reduced actions combined with 3D…

For a complete understanding of the QCD phase diagram it is important to connect first-principle thermodynamic calculations to experimental data from the RHIC Beam Energy Scan and the future experimental facilities FAIR, GSI, and NICA,…

We derive the two-particle fluctuation correlator in a thermal gas of pi-mesons to the lowest order in an interaction due to a resonance exchange. A diagrammatic technique is used. We discuss how this result can be applied to event-by-event…

We propose to describe the time evolution of quasi-stationary fluctuations near QCD critical point by a system of stochastic Boltzmann-Langevin-Vlasov-type equations. We derive the equations and study the system analytically in the…

Two-particle correlations are a widely used tool for studying relativistic nuclear collisions. Multiplicity fluctuations comparing charge and particle species have been studied as a possible signal for Quark-Gluon Plasma (QGP) and the QCD…

Relativistic hydrodynamics is essential to our current understanding of nucleus-nucleus collisions at ultrarelativistic energies (current experiments at the Relativistic Heavy Ion Collider, forthcoming experiments at the CERN Large Hadron…

We introduce a model for the real-time evolution of a relativistic fluid of quarks coupled to non-equilibrium dynamics of the long wavelength (classical) modes of the chiral condensate. We solve the equations of motion numerically in 3+1…

A very intuitive description of nucleus-nucleus collision phenomena is provided by the relativistic fluid dynamics. We consider a 1+1 dimensional relativistic imperfect fluid flow to approximate the high energy heavy ion collision. The…

Dynamical fluctuations in global conserved quantities such as baryon number, strangeness, or charge may be observed near a QCD critical point. Results from new measurements of dynamical $K/\pi$, $p/\pi$, and $K/p$ ratio fluctuations are…

The current understanding of finite temperature phase transitions in QCD is reviewed. A critical discussion of refined phase transition criteria in numerical lattice simulations and of analytical tools going beyond the mean-field level in…

These introductory lectures present a broad overview of the physics of high parton densities in QCD and its application to our understanding of the early time dynamics in heavy ion collisions.

QCD matter at finite temperature and density is a subject that has witnessed very impressive theoretical developments in the recent years. In this review I will discuss some new insights on the microscopic degrees of freedom of the QCD…

We study the fluctuations and correlations of conserved charges, i.e. the baryon number, electric charge and the strangeness at finite temperature and nonzero baryon chemical potential with an effective model. The fluctuations are…

We have used the relativistic second-order causal viscous hydrodynamics equipped with an equation of state which includes the QCD critical point to study the propagation of linear and nonlinear perturbations in quark gluon plasma created in…

Lattice QCD allows us to simulate QCD at non-zero temperature and/or densities. Such equilibrium thermodynamics calculations are relevant to the physics of relativistic heavy-ion collisions. I give a brief review of the field with emphasis…