Violations of bulk-edge correspondence for topological insulators

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Tom Stoiber, Yeshiva University

*note location change*

Jadwin Hall 4th floor PGI Open Space

Bulk-edge correspondence is an important part of the theory of topological insulators which relates topological invariants in the bulk of an insulator to those of its topologically protected edge modes. Despite numerous rigorous proofs, this paradigm has recently been shown to fail in continuum models for topological phases where the Hamiltonians are differential operators with certain local boundary conditions. In this talk I want to examine some of those examples, explain why they are not captured by existing rigorous results and discuss a more general formulation of bulk-edge correspondence which makes sense of some of these apparent violations. This is joint work with Johannes Kellendonk.