Over the past ten years tremendous progress has been achieved in quantum field theory thanks to the realization that symmetries can be interpreted in terms of the action of topological defects on the space of operators. This gives a generalization of the notion of symmetries, explicitly realized in many instances exploiting Lagrangian field theory techniques, uncovering a rich and unexpected landscape of physical effects in condensed matter, high energy physics, and quantum gravity. This conference will bring together the major experts in the subject, and strives to be an opportunity for participants to quickly get up to speed with the most recent advances and open problems in the field.