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This course is intended to give participants (graduates, researchers and industrial professionals) a solid background in tribology and surface interactions. It covers the fundamentals concepts of tribology including surfaces, contact mechanics, friction, lubrication and wear, the description of different techniques for multiscale wear analysis (experimental and computational) and application examples illustrating how to use the theoretical background in engineering practice. At the end of the course, participants will have the tools to identify and to approach tribological systems combined with appropriate material selection and surface design.

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,    Physique mathématique