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Phase transitions are ubiquitous in systems consisting of a large number of interacting components, which can be as simple as a gas or as complex as human society. Often one observes intriguing associated dynamic phenomena such as a separation of time scales and metastability. A classical example is the liquid-gas transition of water, which exhibits metastability of supersaturated vapour over relatively long time scales, followed by a rapid transition to the liquid phase. A phenomenological description of such metastable states goes back to van der Waals theory of non-ideal gases. Besides a proper description of the states, the relevant dynamic aspects are the lifetimes of the states and how transitions occur between them. In reality transitions are often triggered by small impurities (causing e.g. droplet nucleation in vapour), and in mathematical models this is often achieved by adding randomness to dynamics. Stochastic particle systems, where idealized particles move and interact in a discrete (lattice) geometry, provide therefore a very natural class of models to study and understand the dynamics of such transitions and the concept of metastability.A mathematically rigorous approach poses very challenging research questions, and is an active area of modern probability theory where significant recent progress has been achieved. The proposed research builds on these developments and aims towards a full rigorous understanding of a condensation transition in zero-range processes, a particular class of stochastic particle systems which has attracted recent research interest in theoretical physics. Condensation here means, that with increasing density the system switches from a homogeneous distribution of particles to a state where a macroscopic fraction of all the particles condenses on a single lattice site. Zero-range processes are therefore used as generic models of condensation phenomena with applications ranging from clustering of granular materials to the formation of giant hubs in complex network dynamics. They are also of theoretical interest as effective models of domain wall dynamics separating different phases in more general systems, explaining phenomena like the formation of traffic jams on highways.Zero-range processes show a very rich critical behavior with interesting dynamic phenomena on several time scales including metastability, which have been understood on a heuristic level in statistical physics, inspiring many ideas in this proposal. The aim of the project is to underpin these findings with rigorous probabilistic results by proving scaling limits for the dynamics of effective observables on several different time scales. These concrete outcomes will be put into a wider context and will lead to methodological advances, by improving and generalizing recent mathematical techniques and understanding the exact conditions of validity of heuristic arguments used for predictions. Also conceptual insights are invisaged, by exploring new approaches for the mathematical characterization of metastability phenomena in stochastic particle systems.