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  1. ; (, International Mathematics Research Notices)
    Abstract We prove that if the boundary of a topological insulator divides the plane into two regions, each containing arbitrarily large balls, then it acts as a conductor. Conversely, we construct a counterexample to show that topological insulators that fit within strips do not need to admit conducting boundary modes. This constitutes a new setup where the bulk-edge correspondence is violated. Our proof relies on a seemingly paradoxical and underappreciated property of the bulk indices of topological insulators: they are global quantities that can be locally computed. 
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  2. ; ; (, Communications on Pure and Applied Mathematics)
    Abstract We study the propagation of wavepackets along curved interfaces between topological, magnetic materials. Our Hamiltonian is a massive Dirac operator with a magnetic potential. We construct semiclassical wavepackets propagating along the curved interface as adiabatic modulations of straight edge states under constant magnetic fields. While in the magnetic‐free case, the wavepackets propagate coherently at speed one, here they experience slowdown, dispersion, and Aharonov–Bohm effects. Several numerical simulations illustrate our results. 
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  3. ; (, Journal of Spectral Theory)
    In this paper, we prove pure point spectrum for a large class of Schrödinger operators over circle maps with conditions on the rotation number going beyond the Diophantine. More specifically, we develop the scheme to obtain pure point spectrum for Schrödinger operators with monotone bi-Lipschitz potentials over orientation-preserving circle homeomorphisms with Diophantine or weakly Liouville rotation number. The localization is uniform when the coupling constant is large enough. 
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  4. ; ; ; ; ; (, SIAM Journal on Mathematical Analysis)
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