In this contribution we will address a few selected topics concerning the search for a phase structure in the QCD phase diagram. We will extract some constraints for model calculations from basic consideration about the QCD phase diagram. We will also discuss to what extent lattice calculations may be compared to measurements, and what the necessary corrections will be. Finally we will address the dynamics associated with the spinodal break up due to a first order phase transition.

These lectures are an attempt to a pedagogical introduction into the elementary concepts of chiral symmetry in nuclear physics. Effective chiral models such as the linear and nonlinear sigma model will be discussed as well as the essential ideas of chiral perturbation theory. Some applications to the physics of ultrarelativistic heavy ion collisions will be presented.

We will provide a review of some of the physics which can be addressed by studying fluctuations and correlations in heavy ion collisions. We will discuss Lattice QCD results on fluctuations and correlations and will put them into context with observables which have been measured in heavy-ion collisions. Special attention will be given to the QCD critical point and the first order co-existence region, and we will discuss how the measurement of fluctuations and correlations can help in an experimental search for non-trivial structures in the QCD phase diagram.

In this contribution we present an alternative scenario for the large elliptic flow observed in relativistic heavy ion collisions. Motivated by recent results from Lattice QCD on flavor off-diagonal susceptibilities we argue that the matter right above Tc can be described by single-particle dynamics in a repulsive single-particle potential, which in turn gives rise to elliptic flow. These ideas can be tested experimentally by measuring elliptic flow of heavy quarks, preferably via the measurement of J / Ψ elliptic flow. © 2009 Elsevier B.V. All rights reserved.