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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.

Physique des hautes énergies, des particules et des champs,    Cours et événements pour étudiants en physique

The aim of the topical workshop is to bring together particle physicists, string theorists and mathematicians working on elliptic and higher functions, with the goal of providing a framework for fruitful discussions bridging between different languages and approaches in physics and mathematics.