Coarse index theory and the gap-filling phenomenon

Guo Chuan Thiang  (北京大学国际数学研究中心)

10:00-11:00, September 22, 2020   Zoom 467 658 1686

Abstract:

Magnetic Laplacians on non-compact non-positively curved manifolds, can acquire isolated eigenvalues called Landau levels, lying below the continuous spectrum. Physical intuition from the quantum Hall effect suggests that these Landau levels are ``topological'', and predicts that the spectral gaps between them are filled up whenever a boundary is introduced. We prove this gap-filling result for the hyperbolic plane, using coarse index theory methods. Along the way, we obtain a more concrete meaning of the coarse index of the Dirac operator, and its ``dimensional reduction'' to the boundary. Joint work with M. Ludewig.

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