By Roberto Fernandez, Utrecht University

Non-Gibbsian measures were initially studied in relation to renormalization transformations.  In this setting they emerged via phase transitions in the ensemble of original (internal) spins conditioned to a particular renormalized configuration. Later, the same mathematical techniques led to proofs that low-temperature Ising measures subjected to a high-temperature spin-flip evolution can become non-Gibbsian after a finite time. These proofs, however, amount to a "static" view of the evolution as projections of systems with one additional (time) dimension. This was an unsatisfactory state of affairs that did not seem to lead to a truly dynamical understanding of the onset of non-Gibbsianness. As a response to this criticism, in the last few years a new paradigm has been developed in which Gibbs-non-Gibbs transitions are related to changes in the large-deviation rates of conditioned evolutions of measures: Rates with multiple global minima lead to non-Gibbsianness. I will present the main ideas behind this new approach and report on rigorous results for mean-field and local mean-field models.