Title: Topological Insulators at Strong Disorder
Speaker: Emil Prodan
Date: Tuesday, June 23, 2015
Time: 11:00am – 12:30pm
Place: Seminar Room 313, Simons Center
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Abstract: In this talk I will present some recent advances in the analysis of topological insulators at strong disorder. The setting is that of operator algebras, both C-star and von-Neumann, K-theory and non-commutative geometry. In the first part, I will summarize an extension to higher space dimensions, both even and odd, of the work by Bellissard et al. on the integer quantum Hall effect. The main products are bulk topological invariants for the complex classes of topological insulators, whose integer values can change only if the Fermi level crosses a region of delocalized energy spectrum. In the second part, I will present an extension to higher dimensions, both even and odd, of the work by Kellendonk et al. on the bulk-boundary correspondence principle for the integer quantum Hall effect. The main products are boundary topological invariants for the complex classes of topological insulators, defined in the presence of strong disorder and arbitrary homogeneous boundaries, and a proof of equality between the bulk and boundary invariants. Furthermore, it is shown that a non-trivial common value of the invariants ensures the delocalized character of the boundary states, which is the defining property of topological insulators. This work was in collaboration with Jean Bellissard and Hermann Schulz-Baldes.