This research is devoted to the theoretical understanding of the equilibrium and nonequilibrium dynamic behavior of glassy materials. This broad class of systems includes many industrially relevant materials window glass, binary fluid mixtures, superconductors, complex fluids (foams, colloids) and granular materials; at the same time, it presents exciting challenges for fundamental research. However, up to now, the most important development have been achieved in the mean-field approximation, which is only exact in the limit of infinite spatial dimensions. Understanding the generic features of systems with slow dynamics is thus an important and actual challenge for condensed matter theory. The objective of the research is to bring new results to the field, by investigating the crucial role (but largely unexplored) role of thermal activation, and by giving a 'real-space' description (relevant length scales and topology) of the dynamics. For this purpose, three carefully chosen spin models will be investigated, by a combination of analytical and numerical methods. These research avenues arise naturally in the rapidly developing field of glassy dynamics of `complex systems´ and are expected to yield important new insights into the theoretical and experimental behaviour of glassy materials and into the development of a no equilibrium statistical mechanics for those systems. The research focuses on a very open subject, relating many important issues both for fundamental research and for applications. Hence, it represents an exciting challenge. As a first postdoctoral experience abroad, this project will thus provide me with training in research in competitive international environment. Skills acquired during my Ph-D will be very useful, but I will also become more familiar and independent with these different techniques, simultaneously broadening my field of expertise and learning new analytical techniques, through the development of new collaborations. The Theoretical Condensed Matter Physics Group in Oxford appears as natural choice, since it presents a convergence on both thematic and technical aspects of the project. Oxford is internationally renowned, with expertise in many relevant areas in condensed matter and no equilibrium statistical physics, and benefits from many seminars and a large number of visiting scientists. Joining Oxford University, one of the most important poles of research in theoretical physics is of primary importance for a young postdoc, and is a crucial step for a successful career in physics.