Tom Stoiber

I am a Visiting Assistant Professor at the University of California, Irvine, working with Svetlana Jitomirskaya.

Before that I was postdoctoral fellow at Yeshiva University, New York, working with Emil Prodan and funded by a Walter-Benjamin fellowship by the German Research Foundation. And before that I obtained a doctoral degree in mathematical physics at the Friedrich-Alexander University Erlangen-Nürnberg under Hermann Schulz-Baldes.

I am working in mathematical physics applied to the study of topological quantum systems and metamaterials. My research mainly revolves around operator-algebraic methods, in particular operator K-theory, index theory and noncommutative geometry, but also involves various flavors of functional analysis, operator theory and harmonic analysis.

Publications

My monograph with H. Schulz-Baldes, Harmonic Analysis in Operator Algebras and its Applications to Index Theoryand Topological Solid State Systems, Mathematical Physics Studies (Springer, Oct. 2022), (click here for the preprint version)

My dissertation: Index theory and bulk-boundary correspondence of topological insulators and semimetals, doctoral dissertation, Friedrich-Alexander-Universitat Erlangen-Nürnberg (full text)

Papers

with J. Kellendonk, The role of self-adjoint extensions in the bulk-edge correspondence (2025).
Spectral continuity for étale groupoids with the Rapid decay property (2025).
with D. Polo Ojito, E. Prodan, On Frustration-Free Quantum Spin Models (2025).
with D. Polo Ojito, E. Prodan, Invariant measures on the transversal hull of cone semigroups and some applications, (2025).
with D. Polo Ojito, E. Prodan, A space-adiabatic approach for bulk-defect correspondences in lattice models of topological insulators (2024).
A spectral localizer approach to strong topological invariants in the mobility gap regime (2024). Comm. Math. Phys. 406 (8), 184 (2025).
with D. Polo Ojito, E. Prodan, C*-framework for higher-order bulk-boundary correspondences, Comm. Math. Phys. 406, 184 (2025).
with F. Lux, S. Wang, G. Huang, E. Prodan, Topological Spectral Bands with Frieze Groups, J. Math. Phys. 65, 063502 (2024)
with H. Schulz-Baldes, The generators of the K-groups of the sphere, Expositiones Mathematicae 41, 125519 (2023)
with H. Schulz-Baldes, Spectral localization for semimetals and Callias operators, J. Math. Phys. 64, 081901 (2023).
with H. Schulz-Baldes, Callias-type operators associated to spectral triples, J. Noncommut. Geom. 17 (2023), 527–572
with H. Schulz-Baldes, Invariants of disordered semimetals via the spectral localizer, EPL 136, 27001 (2021).
with H. Schulz-Baldes, The spectral localizer for semifinite spectral triples, Proc. Amer. Math. Soc. 149, 121-134 (2021).

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