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BIRS Workshop Lecture Videos

Index theory and topological phases of aperiodic lattices Mesland, Bram


A Delone set is a uniformly discrete and relatively dense subset of Euclidean space $\mathbb{R}^{d}$. As such they constitute a mathematical model for a general solid material. By choosing an abstract transversal for the translation action on the orbit space of the Delone set, one obtains an etale groupoid. In the absence of a $\mathbb{Z}^d$-labelling, the associated groupoid C*-algebra replaces the crossed product algebra as the natural algebra of observables. The K-theory of the groupoid C*-algebra is a natural home for the formulation of the bulk-boundary correspondence for topological insulators as well as a source for numerical invariants of (weak) topological phases. This is joint work with Chris Bourne

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