Quantum structures in Algebra and Geometry

Recent advances in the band theory of crystalline materials have singled out topology as a key ingredient in the modern classification of matter, with major impact on measurable electronic properties. Topological band theory has also grown into an emerging paradigm in many areas of physics, and is now used to characterize metamaterials, including photonic, atomic, acoustic, and elastic systems, in both the quantum and classical regimes. As our understanding of topology in physics widens, the incorporation of out-of-equilibrium phenomena is gaining in importance.