nLab Hermann Schulz-Baldes

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Selected writings

On the bulk-edge correspondence in integer quantum Hall systems:

• Johannes Kellendonk, Thomas Richter, Hermann Schulz-Baldes: Edge current channels and Chern numbers in the integer quantum Hall effect, Rev. Math. Phys. 14 1 (2002) 87–119 [doi:10.1142/S0129055X02001107]

• Johannes Kellendonk, Hermann Schulz-Baldes: Quantization of edge currents for continuous magnetic operators, J. Funct. Anal. 209 (2004) 388-413 [doi:10.1016/S0022-1236(03)00174-5, arXiv:math-ph/0405021]

• Johannes Kellendonk, Hermann Schulz-Baldes: Boundary maps for $C^\ast$-crossed products with $\mathbb{R}$ with an application to the quantum Hall effect, Commun. Math. Phys. 249 (2004) 611-637 [doi:10.1007/s00220-004-1122-7, arXiv:math-ph/0405022]

On topological insulators with focus on edge modes and the bulk-boundary correspondence via topological K-theory and in the presence of disorder:

• Emil Prodan, Hermann Schulz-Baldes: Bulk and Boundary Invariants for Complex Topological Insulators – From K-Theory to Physics, Springer (2016) [doi:10.1007/978-3-319-29351-6]

Explicit formulas for Dirac operators parameterized by n-spheres and regarded as Fredholm operators representing topological K-theory, with an eye towards the K-theory classification of topological phases of matter:

• Hermann Schulz-Baldes, Tom Stoiber: The generators of the $K$-groups of the sphere, Expositiones Mathematicae 41 4 (2023) 125519 [arXiv:2403.18944, doi:10.1016/j.exmath.2023.125519]

On spectral flow of self-adjoint Fredholm operators:

• Nora Doll, Hermann Schulz-Baldes, Nils Waterstraat: Spectral Flow — A Functional Analytic and Index-Theoretic Approach, Studies in Mathematics 94, De Gruyter (2023) [doi:10.1515/9783111172477, hdl:20.500.12657/63798]

On topological indices in solid state physics (topological phases of matter):

• Hermann Schulz-Baldes: Topological indices in condensed matter, in: Encyclopedia of Mathematical Physics 2nd ed, 1 (2025) 17-26 [arXiv:2403.18948, doi:10.1016/B978-0-323-95703-8.00041-0]

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