About me

Welcome! I'm a research mathematician at the University of Sydney. Most of my work sits firmly inside pure mathematics: representation theory, categorical algebra, diagrammatics, monoidal categories, and quantum topology. I enjoy moving between algebra, category theory, topology, and combinatorics, and I am especially interested in how structure, symmetry, growth, and analytic phenomena interact.

Alongside this, I have been broadening my range in a way that remains thoroughly mathematically driven. Rather than treating computation as something separate from pure mathematics, I use it as another lens on hard algebraic, categorical, and topological problems. This includes big-data projects on Kazhdan–Lusztig theory and quantum knot invariants, reinforcement learning for unknotting and unknotting-number questions, work on representation gaps motivated in part by cryptography, and ongoing interests in analytic aspects of algebra and category theory.

Recent examples of this broader direction include Big data approach to Kazhdan–Lusztig polynomials, Big data comparison of quantum invariants, On detection probabilities of link invariants, On knot detection via picture recognition, and RL unknotter, hard unknots and unknotting number. The common theme is not a move away from pure mathematics, but an attempt to bring pure-mathematical ideas into conversation with modern computation, data analysis, and algorithmic experimentation.

I'm always happy to hear from people with related interests: whether your angle is algebraic, topological, computational, or somewhere in between. Feel free to reach out at daniel.tubbenhauer@sydney.edu.au.

★Current highlights

  • Pure mathematics: categorical representation theory, monoidal categories, tensor products, diagram algebras, quantum topology, and analytic aspects of algebra and category theory.
  • Big data: large-scale and exploratory analyses of Kazhdan–Lusztig polynomials and knot/link invariants.
  • Machine learning: picture recognition for knots and reinforcement learning pipelines for simplifying knot diagrams.
  • Cryptography: representation gaps of monoids and monoidal categories, with diagrammatic examples motivated by post-linear-attack questions.

✉Contact data

Name: Daniel Tubbenhauer (Dani)
Position: ARC Future Fellow, University of Sydney profile
CV: Click
Email: daniel.tubbenhauer@sydney.edu.au or dtubbenhauer@gmail.com
Business card: Click
Keywords: categorical and 2-representations, categorical algebra, monoidal and tensor categories, representation theory, quantum algebra, knot theory, quantum topology, analytic aspects of algebra and category theory, big data, machine learning, reinforcement learning, and cryptography
Metrics: See Google scholar
Recent directions: big data for Kazhdan–Lusztig theory and knot invariants, analytic and asymptotic questions in algebra and category theory, RL unknotting, knot detection from images, and representation gaps in cryptography
How to pronounce my name:
Grant selection: Future fellowship
Discovery project
Address:
The University of Sydney
School of Mathematics and Statistics
F07 - Carslaw Building
Office Carslaw 827
NSW 2006
Australia
Phone: +61(0)422528844
Pronouns: they/them
Misc: I support and I am part of Pride; Click; I do not need honorific titles - they are decorations only