Quantum Topology

Quantum topology explores how the properties of materials and systems are shaped by their underlying geometric and topological features, especially at the quantum level. It studies how certain electronic states are protected by these properties, leading to robust phenomena like conducting edges in insulators or stable quantum states useful for quantum computing. Unlike conventional materials, where behavior depends on specific details, topological materials have characteristics tied to their overall shape or structure, making them resistant to disruptions. This field blends advanced mathematics with quantum physics to discover new states of matter with promising technological applications.