Recent Progress in Topological Insulators

23.07.2025, 14:00 - 16:00 (special session)  –  Campus Golm, Building 9, Room 2.22 and via Zoom
Institutskolloquium

Nora Doll (Uni Halle), Giuseppe De Nittis (Santiago de Chile)

14:00  Nora Doll (Halle):  Skew localizer for real index pairings.
14:45  Tea and Coffee Break
15:15  Giuseppe De Nittis (Santiago de Chile):  Spectral analysis of sub-Riemannian Laplacians and Weyl measure.

Nora Doll (University of Halle):  Skew localizer for real index pairings.

Abstract:     In this talk index pairings of a projection and a unitary where both, the projectio and the unitary fulfil real symmetry relations are considered. For a given combination of symmetries the integer-valued index of the pairing vanishes, but there may be a Z2-index given by the dimension of its kernel, modulo 2. The aim is then to construct a finite-dimensional real skew-adjoint matrix called the skew localizer for these pairings and to show that the Z2-index can be computed as the sign of the Pfaffian of the skew localizer.
    

Giuseppe De Nittis (Catholic University of Chile, Santiago de Chile):  Topological phases of non-interacting systems: A general approach based on states.

Abstract:     In this work we provide a classification scheme for topological phases of certain systems whose observable algebra is described by trivial C*-bundles. The classification is based on the study of the homotopy classes of configurations, which are maps from a quantum parameter space to the space of pure states of a reference fiber C*-algebra. Both the quantum parameter space and the fiber algebra are naturally associated with the observable algebra. A list of various examples described in the last part shows that the common classification scheme of non-interacting topological insulators of type A is recovered inside this new formalism.
    

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