Mathematisches Kolloquium

Zusammenfassung: Topological insulators are materials, which are conducting at their edges, though not in the bulk. Their essential physical properties take the form of an index, often associated to the Hamiltonian. "Topological" simply refers to the fact that indices remain invariant under continuous changes. An early type of such insulators occurred in connection with the Quantum Hall effect, which has been the source of various mathematical developments. We shall review two indices, associated with the bulk and the edge of the samples and illustrate their equivalence and some application to graphene. A different, more recent type of insulators retains (fermionic) time-reversal invariance and is further classified according to a Z2 index. We discuss its various guises (Pfaffian and Kramers indices) and the bulk-edge duality. (Based on work with M. Porta, A. Agazzi, J.-P. Eckmann)

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