Homepage Daniel Tubbenhauer

Daniel (Dani) Tubbenhauer

Welcome! I am a research mathematician working in representation theory, categorical algebra, diagrammatics, monoidal categories, and quantum topology. I like situations where pictures, algebraic rules, categorical structures, and computations are different languages for the same phenomenon.

The current program is broad by design: pure mathematics at the center, with computation, data, algorithms, and topology used as lenses for finding structure rather than as replacements for proof.

Current directions

Pure mathematics

Symmetry, structure and invariants through categorical representation theory, monoidal categories, Hecke categories, diagrammatics and quantum topology.

Computation

Computer algebra and large datasets as mathematical instruments: examples, conjectures, growth laws, and tests for where intuition breaks.

AI and machine learning

Machine learning and AI-flavored experimentation for knot diagrams, picture recognition, reinforcement learning, and large-scale searches in diagrammatic settings.

Contact and quick 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
Metrics: Google Scholar
Grants: Future Fellowship, Discovery Project
How to pronounce my name:

Address, keywords, and misc

Address:

The University of Sydney
School of Mathematics and Statistics
F07 - Carslaw Building, Office Carslaw 827
NSW 2006, Australia
Phone: +61(0)422528844

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.
Pronouns: they/them
Misc: I support and I am part of Pride

; Click. I do not need honorific titles; they are decorations only, but I am an associate professor.

Visual mathematics, videos, and some selfies

Much of my mathematics sits between pictures and abstraction. Knots, webs, cells, strands and diagrammatic categories are often part of the formal language: moving a strand, simplifying a diagram, or composing pictures can be an algebraic operation.

The videos below are part of the same philosophy. They are attempts to make algebra, topology, categories and computation visible without pretending that the subject is less strange than it is.