Symmetry is a powerful tool for organizing physical phenomena, anchoring our understanding of the laws of nature. Since the emergence of groups and representations as the correct language to describe symmetries in geometry and mechanics, the notion of symmetry has evolved dramatically, galvanized by advances in both mathematics and physics. Recently, much of this evolution has been driven by the quest to achieve a deeper understanding of quantum field theory — the universal language of modern theoretical physics. This collaboration brings together a group of physicists and mathematicians, working across disciplinary boundaries, to unlock the power of symmetry in its broadest, most general form.
From a modern point of view, quantum field theory associates to every symmetry a topological defect, which acts on local and extended observables. This understanding has recently led to the discovery of new higher notions of symmetry, which in turn has shed new light on some of the most mysterious and profound phenomena described by quantum field theory, including color confinement in non-abelian gauge theories and duality. The deep link between symmetry and topology finds its natural expression in the mathematics of topological quantum field theory, such as the modular tensor categories that describe invariants of knots and the long-distance physics of anyons. Recent advances have centered on the rich categorical structure of various defects and how it encodes the fundamental idea of locality, as expressed by the cobordism hypothesis.
Our collaboration grows out of the synergy between these areas of physics and mathematics, weaving together cutting-edge developments.