We study topological insulators, regarded as physical systems giving rise to topological
invariants determined by symmetries both linear and anti-linear. Our perspective is that of …

We provide a constructive proof of exponentially localized Wannier functions and related
Bloch frames in 1-and 2-dimensional time-reversal symmetric (TRS) topological insulators …

We study the application of Kasparov theory to topological insulator systems and the bulk–
edge correspondence. We consider observable algebras as modelled by crossed products …

We give a topological classification of quantum walks on an infinite 1D lattice, which obey
one of the discrete symmetry groups of the tenfold way, have a gap around some …

In a basic framework of a complex Hilbert space equipped with a complex conjugation and
an involution, linear operators can be real, quaternionic, symmetric or anti-symmetric, and …

We study a wide class of topological free-fermion systems on a hypercubic lattice in spatial
dimensions d≥ 1. When the Fermi level lies in a spectral gap or a mobility gap, the …

We provide a classification of translation invariant one-dimensional quantum walks with
respect to continuous deformations preserving unitarity, locality, translation invariance, a …

Real index pairings of projections and unitaries on a separable Hilbert space with a real
structure are defined when the projections and unitaries fulfill symmetry relations invoking …

We study disordered topological insulators with time reversal symmetry. Relying on the
noncommutative index theorem which relates the Chern number to the projection onto the …

In order to study continuous models of disordered topological phases, we construct an
unbounded Kasparov module and a semifinite spectral triple for the crossed product of a …