Arun Debray

a.debray@gmail.com
 

Hello! I am a mathematician, working in algebraic topology with an eye towards quantum field theory and condensed-matter physics. Since Fall 2024, I have been an Assistant Professor at the University of Kentucky. From 2021–2024, I was a postdoc at Purdue University. Before that, I was a graduate student at UT Austin, advised by Dan Freed. Before grad school, I was an undergrad at Stanford University, graduating in 2015.

I find mathematics so fascinating partly because different subfields and concepts are very inter­connected, reinforcing and influencing each other.
“Good mathematicians see analogies between theorems or theories; the very best ones see analogies between analogies.” – Stefan Banach

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Papers and Preprints

  1. Hyperkähler bases for six rational bordism theories, joint with Jonathan Buchanan, Cameron Krulewski, and Stephen McKean. 2026. arXiv:2601.18701.

  2. How to Build Anomalous (3+1)d Topological Quantum Field Theories, joint with Weicheng Ye and Matthew Yu. 2025. arXiv:2510.24834.

  3. Exploring Pintopia: Reflection Branes, Bordisms, and U-Dualities, joint with Vivek Chakrabhavi, Markus Dierigl, and Jonathan J. Heckman. 2025. arXiv:2509.03573.

  4. Cobordism Utopia: U-Dualities, Bordisms, and the Swampland, joint with Noah Braeger, Markus Dierigl, Jonathan J. Heckman, and Miguel Montero. Accepted for publication, Adv. Theor. Math. Phys. 2025. arXiv:2505.15885.

  5. Global Structure in the Presence of a Topological Defect, joint with Weicheng Ye and Matthew Yu. 2025. arXiv:2501.18399.

  6. Type IIA string theory and tmf with level structure, joint with Matthew Yu. 2024. arXiv:2411.07299.

  7. Weak topological phases in the presence of interactions, joint with Omar Antolín Camarena, Cameron Krulewski, Natalia Pacheco-Tallaj, Daniel Sheinbaum, and Luuk Stehouwer. 2024. arXiv:2410.10031.

  8. Smith homomorphisms and Spinh structures, joint with Cameron Krulewski. Proc. Amer. Math. Soc. volume 153, pp. 897–912. 2025. arXiv:2406.08237.

  9. The Smith fiber sequence of invertible field theories, joint with Sanath K. Devalapurkar, Cameron Krulewski, Yu Leon Liu, Natalia Pacheco-Tallaj, and Ryan Thorngren. Comm. Math. Phys. volume 407, number 25, 2026. arXiv:2405.04649.

  10. Differential cohomology (encyclopedia article). In Encyclopedia of Mathematical Physics, 2nd (ed. Richard Szabo and Martin Bojowald), Academic Press, 2025. arXiv:2312.14338.

  11. Bosonization and Anomaly Indicators of (2+1)-D Fermionic Topological Orders, joint with Weicheng Ye and Matthew Yu. Comm. Math. Phys. volume 406, number 178, 2025. arXiv:2312.13341.

  12. Global anomalies & bordism of non-supersymmetric strings, joint with Ivano Basile, Matilda Delgado, and Miguel Montero. JHEP, volume 2024, number 92. 2024. arXiv:2310.06895.

  13. A Long Exact Sequence in Symmetry Breaking: order parameter constraints, defect anomaly-matching, and higher Berry phases, joint with Sanath K. Devalapurkar, Cameron Krulewski, Yu Leon Liu, Natalia Pacheco-Tallaj, and Ryan Thorngren. JHEP, volume 2025, number 7. 2025. arXiv:2309.16749.

  14. Adams spectral sequences for non-vector-bundle Thom spectra, joint with Matthew Yu. 2023. arXiv:2305.01678.

  15. Bordism for the 2-group symmetries of the heterotic and CHL strings. In Higher Structures in Geometry, Topology and Physics, Contemp. Math. volume 802, pp. 227–297, 2024. arXiv:2304.14764. Errata.

  16. The Chronicles of IIBordia: Dualities, Bordisms, and the Swampland, joint with Markus Dierigl, Jonathan J. Heckman, and Miguel Montero. Adv. Theor. Math. Phys. volume 28, number 3, pp. 805–1025. 2024. arXiv:2302.00007.

  17. What bordism-theoretic anomaly cancellation can do for U, joint with Matthew Yu. Comm. Math. Phys. volume 405, number 154, 2024. arXiv:2210.04911.

  18. Constructing the Virasoro groups using differential cohomology, joint with Yu Leon Liu and Christoph Weis. Int. Math. Res. Not., volume 2023, number 21, pp. 18537–18574. 2023. arXiv:2112.10837.

  19. The anomaly that was not meant IIB, joint with Markus Dierigl, Jonathan J. Heckman, and Miguel Montero. Fortschr. Phys. volume 70, issue 1. 2022. arXiv:2107.14227.

  20. Stable diffeomorphism classification of some unorientable 4-manifolds. Bull. London Math. Soc., volume 54, issue 6, pp. 2219–2231. 2022. arXiv:2102.03965.

  21. Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle, 2021. arXiv:2102.02941. Errata.

  22. The low-energy TQFT of the generalized double semion model. Comm. Math. Phys. volume 375, issue 2, pp. 1079–1115. 2020. arXiv:1811.03583.

  23. The Arf-Brown TQFT of Pin− Surfaces, joint with Sam Gunningham. In Topology and Quantum Theory in Interaction, Contemp. Math. volume 718, pp. 49–87. 2018. arXiv:1803.11183.

Books

  1. Differential Cohomology: Categories, Characteristic Classes, and Connections, edited jointly with Araminta Amabel and Peter J. Haine. 2021. arXiv:2109.12250.

Other