Date: 3 June 2025 - 6 June 2025
Topological insulators are materials that are conducting at their edge, though not in the bulk. Their essential physical properties are encoded by an index. After reviewing the historical origins, and the Quantum Hall effect in particular, the appropriate indices will be discussed (Chern numbers, index of a pair of projections), as well as bulk-edge correspondence. Thereafter symmetry protected topological insulators will be addressed. The focus will be on symmetries like time-reversal and particle-hole conjugation and, correspondingly, on the Quantum Spin Hall effect and Majorana zero modes in superconductors, in physical dimensions d=2 and 1, respectively. More broadly, the Kitaev table describes the kind of indices that occur in elation to many more symmetries, in any dimension d, and its derivation will be treated. Special topics beyond the above framework, such as time-dependent systems (Floquet or quantum pumps) or classical systems (hydrodynamics) may occur too, as time permits.