3 papers
math.QA2025
Quantum topology without topology
Daniel Tubbenhauer
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bri…
math.RT2025
Representation gaps of rigid planar diagram monoids
Willow Stewart, Daniel Tubbenhauer
We define non-pivotal analogs of the Temperley-Lieb, Motzkin, and planar rook monoids, and compute bounds for the sizes of their nontrivial simple representations. From this, we as…
math.GT2025
Big data comparison of quantum invariants
Daniel Tubbenhauer, Victor Zhang
We apply big data techniques, including exploratory and topological data analysis, to investigate quantum invariants. More precisely, our study explores the Jones polynomial's stru…