Nonequilibrium quantum field theory is needed to understand pressing topical phenomena in high-energy physics related to collisions of heavy nuclei ("Little Bangs'') and early universe cosmology ("Big Bang''). Out-of-equilibrium dynamics is an area which has seen substantially increased theoretical activity in recent years. High-energy particle physicists as well as cosmologists are starting to work with very similar techniques and sometimes even on the same underlying nonequilibrium phenomena. Very similar theoretical issues also arise in other areas, such as ultra-cold quantum gases.

Despite the differences between early-universe and heavy-ion dynamics, there are some remarkable parallels. One example concerns the role of instabilities for the process of thermalization. Plasma instabilities may play an important role in our understanding of RHIC observations. These instabilities lead to exponential growth of occupation numbers in long wavelength modes on time scales much shorter than the asymptotic thermal equilibration time. This is followed by a more complicated period during which power cascades toward shorter wavelengths occur, in a manner reminiscent of, but rather different from, Kolmogorov wave turbulence.

The reheating of the early universe after inflation may exhibit a rather similar pattern. There a tachyonic or parametric resonance instability leads to the exponential growth of occupation numbers, followed again by a slow cascade. Although there are important differences between scalar inflaton dynamics and the more complicated QCD gauge field dynamics, considering both phenomena from a common perspective can be fruitful. The physics of nonequilibrium field dynamics in cosmology and particle physics overlaps also with string theory cosmology. String theory tachyon dynamics is naturally related to effective field theory descriptions of nonequilibrium instabilities.

There has been significant recent progress in understanding nonequilibrium quantum fields using a variety of approaches. Improved approximation techniques (and faster computers) allow one to study questions such as the explosive particle production at the end of the inflationary universe, including the subsequent process of thermalization, with methods based directly on the underlying quantum field theory. In weakly coupled theories, suitable resummation techniques and the formulation of valid effective kinetic theories have allowed first-principles calculations of a variety of transport coefficients in both gauge and non-gauge theories. Real-time numerical simulations based on classical field theory, and Boltzmann-Vlasov kinetic theory, have led to improved understanding of non-Abelian plasma instabilities and inflaton decay and thermalization.

When strong interactions play an important role, as in QCD at accessible energies, reliable approximations are particularly difficult to find. Gauge-string duality offers a novel approach for studying dynamical properties of certain strongly interacting gauge theories. This has led to quantitative results for transport coefficients, energy loss ($dE/dx$) and photoemission spectra in strongly coupled non-Abelian plasma, with promising potential for applications to RHIC physics. It would, of course, be a major advance to be able to perform first-principles simulations of interesting quantum field theories on a Minkowski space-time lattice. Standard simulation techniques based on importance sampling are not applicable to the complex measures needed for real time quantum simulations. An interesting recent development employs stochastic quantization techniques for real times, which do not require a probability distribution, with initial applications to scalar and SU(2) gauge theory.

The goal of this program is to bring together physicists working on different aspects and applications of nonequilibrium quantum field theory, in order to promote cross-fertilization between different areas and to stimulate theoretical advances which can help to address the challenges posed by present-day experiments.