People_
Dr Daniel Tubbenhauer
Pronouns: they/them
Please call me Dani
I do not need honorific titles - they are decorations only.
Please call me Dani
I do not need honorific titles - they are decorations only.
Phone
+61(0)422528844
Address
F07 - Carslaw Building
The University of Sydney
Resume
I am a research mathematician who works at the University of Sydney, at the School of Mathematics and Statistics.
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I am currently working on aspects of 2-representation theory and its applications in cryptography and machine learning, properties of (weighted) KLRW algebras, growth rates in representation theory, dualities in representation theory and I am always interested in a challenge.
My latest research fields include:
-
2-representation theory (“the representation theory of the 21th century”). Ingredients.
(Modular) representation theory, categorical algebra, (higher) category theory, group and semigroup theory. -
Knot homologies, topological quantum field theories, Lie theory and geometry. Ingredients.
Low-dimensional topology, representation theory, quantum Lie theory, quantum or string physics, homological algebra. -
Modular representation theory, in particular of Lie algebras and Lie groups. Ingredients.
Representation theory, Lie theory, diagrammatics, Soergel bimodules. - Diagrammatic representation, especially, their diagrammatic presentations and properties such as cellularity. Ingredients. Classical algebra, monoidal categories, diagram categories, combinatorics.
- Representation theory of monoids and cryptography, when looking at bounds or growth rates of simple representations. Ingredients. Green's cell theory (Green's relations), monoidal categories, diagram categories.
- Representation theory and machine learning, when looking ate equivariant neural networks. Ingredients: Representation theory in piecewise linear.
Please find more information on my personal website: http://www.dtubbenhauer.com/
I would be happy to supervise honours etc. I have list of potential topics online: http://www.dtubbenhauer.com/teaching.html
If you are interested to start working on either of these projects, then feel free to contact me: daniel.tubbenhauer@sydney.edu.au
Timetable
Currently my research focusses on various aspects involving 2-representation theory:
- The abstract theory: allow infinite 2-categories and work in finite characteristic.
- Low-dimensional topology: link homologies and 2-representations of braid groups.
- Cryptography: diagram categories and linear attacks.
- Machine learning via representation theory.
- Representation theory of KLRW algebras and alike.
- Webs in various forms.
I support and I am part of LGBT+.
| Project title | Research student |
|---|---|
| The deformation of cyclotomic KLR algebras | Yuxuan CHENG |
| 2-Representations: a Diagrammatic Approach | Daniel COLLISON |
| Graded Representation Theory of Quiver Hecke algebras | Tao QIN |
| Monoidal Categories and Cryptography | Willow STEWART |
Publications
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Journals
- Bodish, E., Tubbenhauer, D. (2025). On a symplectic quantum Howe duality. Mathematische Zeitschrift, 309(4), Article 68-1-Article 68-59. [More Information]
- Lacabanne, A., Tubbenhauer, D., Vaz, P. (2024). A formula to evaluate type-A webs and link polynomials. Arkiv foer Matematik, 62(1), 83-101. [More Information]
- Mathas, A., Tubbenhauer, D. (2024). Cellularity and subdivision of KLR and weighted KLRW algebras. Mathematische Annalen, 389(3), 3043-3122. [More Information]
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2025
- Bodish, E., Tubbenhauer, D. (2025). On a symplectic quantum Howe duality. Mathematische Zeitschrift, 309(4), Article 68-1-Article 68-59. [More Information]
2024
- Lacabanne, A., Tubbenhauer, D., Vaz, P. (2024). A formula to evaluate type-A webs and link polynomials. Arkiv foer Matematik, 62(1), 83-101. [More Information]
- Mathas, A., Tubbenhauer, D. (2024). Cellularity and subdivision of KLR and weighted KLRW algebras. Mathematische Annalen, 389(3), 3043-3122. [More Information]
- Coulembier, K., Ostrik, V., Tubbenhauer, D. (2024). Growth Rates of the Number of Indecomposable Summands in Tensor Powers. Algebras and Representation Theory, 27, 1033-1062. [More Information]
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2023
- Tubbenhauer, D. (2023). 𝖘𝖑-Web bases, intermediate crystal bases and categorification. Journal of Algebraic Combinatorics, 40(4), 1001-1076. [More Information]
- Lacabanne, A., Tubbenhauer, D., Vaz, P. (2023). Annular webs and Levi subalgebras. Journal of Combinatorial Algebra, 7(3), 283-326. [More Information]
- Lacabanne, A., Tubbenhauer, D., Vaz, P. (2023). Asymptotics in finite monoidal categories. Proceedings of the American Mathematical Society, 10(34), 398-412. [More Information]
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2022
- Tubbenhauer, D., Wedrich, P. (2022). The Center of SL2Tilting Modules. Glasgow Mathematical Journal, 64(1), 165-184. [More Information]
2021
- Mackaay, M., Mazorchuk, V., Miemietz, V., Tubbenhauer, D., Zhang, X. (2021). Finitary birepresentations of finitary bicategories. Forum Mathematicum, 33(5), 1261-1320. [More Information]
- Rose, D., Tubbenhauer, D. (2021). Homflypt homology for links in handlebodies via type a soergel bimodules. Quantum Toplogy, 12(2), 373-410. [More Information]
- Tubbenhauer, D., Wedrich, P. (2021). Quivers For SL2 Tilting Modules. Representation Theory, 25, 440-480. [More Information]
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2020
- Ehrig, M., Tubbenhauer, D. (2020). Algebraic properties of zigzag algebras. Communications in Algebra, 48(1), 11-36. [More Information]
- Tubbenhauer, D. (2020). glN-webs, categorification and Khovanov-Rozansky homologies. Journal of Knot Theory and Its Ramifications, 29(11), 2050074. [More Information]
- Mackaay, M., Mazorchuk, V., Miemietz, V., Tubbenhauer, D. (2020). Trihedral soergel bimodules. Fundamenta Mathematicae, 248(3), 219-300. [More Information]
2019
- Mackaay, M., Mazorchuk, V., Miemietz, V., Tubbenhauer, D. (2019). Simple transitive 2-representations via (co-)algebra 1-morphisms. Indiana University Mathematics Journal, 68(1), 1-33. [More Information]
- Ehrig, M., Tubbenhauer, D., Wilbert, A. (2019). Singular TQFTs, foams and type D arc algebras. Documenta Mathematica, 24, 1585-1655. [More Information]
- Mackaaij, M., Tubbenhauer, D. (2019). Two-color Soergel Calculus and Simple Transitive 2-representations. Canadian Journal of Mathematics-Journal Canadien de Mathematiques, 71(6), 1523-1566. [More Information]
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2018
- Andersen, H., Stroppel, C., Tubbenhauer, D. (2018). Cellular structures using Uq-tilting modules. Pacific Journal of Mathematics, 292(1), 21-59. [More Information]
2017
- Andersen, H., Tubbenhauer, D. (2017). DIAGRAM CATEGORIES FOR Uq-TILTING MODULES AT ROOTS OF UNITY. Transformation Groups, 22(1), 29-89. [More Information]
- Andersen, H., Stroppel, C., Tubbenhauer, D. (2017). Semisimplicity of Hecke and (Walled) Brauer Algebras. Journal of the Australian Mathematical Society, 103(1), 1-44. [More Information]
- Tubbenhauer, D., Vaz, P., Wedrich, P. (2017). Super q-Howe duality and web categories. Algebraic and Geometric Topology, 17(6), 3703-3749. [More Information]
2016
- Rose, D., Tubbenhauer, D. (2016). Symmetric Webs, Jones-Wenzl Recursions, and q-Howe Duality. International Mathematics Research Notices, 2016 (17), 5249-5290. [More Information]
2014
- Tubbenhauer, D. (2014). Virtual Khovanov homology using cobordisms. Journal of Knot Theory and Its Ramifications, 23(9). [More Information]
Selected Grants
2023
- Categorical representation theory and applications, Tubbenhauer D, Australian Research Council (ARC)/Future Fellowships (FT)
"There are two ways to do mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else - but persistent." - based on a quotation from Raoul Bott.
In the media
My YouTube channel: VisualMath