4 papers
Categorification of some Penrose polynomials
D. W. Collison, D. Tubbenhauer
We construct doubly- and triply-graded Penrose-type homologies for ribbon graphs. The construction is a TQFT-valued cube of resolutions built from two-dimensional cobordisms, which…
RL unknotter, hard unknots and unknotting number
Anne Dranowski, Yura Kabkov, Daniel Tubbenhauer
We develop a reinforcement learning pipeline for simplifying knot diagrams. A trained agent learns move proposals and a value heuristic for navigating Reidemeister moves. The pipel…
Möbius Strip Diagram Algebras
D. W. Collison, D. Tubbenhauer
We introduce Möbius strip diagram algebras (and their monoid and categorical versions) as subalgebras of a partition-style diagram calculus in which strands may carry handles and…
Sandwich cellularity and a version of cell theory
Daniel Tubbenhauer
We explain how the theory of sandwich cellular algebras can be seen as a version of cell theory for algebras. We apply this theory to many examples such as Hecke algebras, and vari…