Code, data and reproducibility
Computer talk, but still mathematics
This page collects code, data, interactive experiments and computational companions to my papers.
Most of the projects below are not software packages in the industrial sense. They are research objects: scripts, notebooks, data sets and experiments used to test conjectures, draw pictures, search examples, and keep algebra honest.
For laypersons. The code is the laboratory notebook. In pure mathematics the experiment is often symbolic rather than physical: compute many examples, look for structure, then try to prove the pattern.
Algebra at scale
Kazhdan–Lusztig data, Hecke categories, diagram categories, monoids and tensor powers.
Topology by computation
Knot invariants, diagram simplification, detection probabilities and unknotting experiments.
Machine learning
Picture recognition, reinforcement learning and data-driven tests of mathematical intuition.
Code and friends; general
- My GitHub page has most code files. Get the code: Click
- TeX source files are available for download. Get the code: Click
Code and friends ordered per year
- Many fancy calculations for the paper TBA, joint with Vanessa Miemietz and Marie Roth. Get the code: Click
- Code, data and pictures for the paper Almost all pKL basis elements are bad, joint with Joseph Baine. Get the code: Click
- Code for calculations for the paper Growth in affine Hecke categories, joint with Kevin Coulembier and Jensen O'Sullivan. Get the code: Click
- Presentation generator and more for the paper Presentations for categories of crystals, joint with David He. Get the code: Click
- Code, data and unknotter for the paper RL unknotter, hard unknots and unknotting number, joint with Anne Dranowski and Yura Kabkov. Get the code: Click and Click and Click
- Interactive plots and much more for the paper On detection probabilities of knot invariants, joint with Tuomas Kelomäki, Abel Lacabanne, Pedro Vaz and Victor L. Zhang. Get the code: Click and Click
- Code and data for the paper On knot detection via picture recognition, joint with Anne Dranowski and Yura Kabkov. Get the code: Click
- Magma code for the paper Idempotents, traces, and dimensions in Hecke categories, joint with Ben Elias and Liam Rogel. Get the code: Click
- Mathematica and GAP code for the paper Representations gaps of rigid planar diagram monoids, joint with Willow Stewart. Get the code: Click
- Interactive plots and much more for the paper Big data comparison of quantum invariants, joint with Victor L. Zhang. Get the code: Click and Click
- Details much more for the paper Growth problems in diagram categories, joint with Jonathan Gruber. Get the code: Click
- Data files (and more) of tensor powers of monoid representations, GAP, Python and Magma code and data for the paper Growth problems for representations of finite monoids, joint with David He. Get the code: Click
- Data files (and more) of Kazhdan–Lusztig polynomials, Python code and data for the paper Big data approach to Kazhdan–Lusztig polynomials, joint with Abel Lacabanne and Pedro Vaz. Get the code: Click
- Complex reflection groups categories, SagaMath and Magma code to compute graphs and Koornwinder varieties, related paper On Hecke and asymptotic categories for complex reflection groups, joint with Abel Lacabanne and Pedro Vaz. Get the code: Click
- Piecewise linear representation theory, runs in html on this webpage, related paper Equivariant neural networks and piecewise linear representation theory, joint with Joel Gibson and Geordie Williamson. Get the code: Click
- Tensor powers of SL2, Magma code and Mathematica notebook to compute asymptotics for growth rates, related paper Fractal behavior of tensor powers of the two dimensional space in prime characteristic, joint with Kevin Coulembier, Pavel Etingof and Victor Ostrik. Get the code: Click
- Growth and monoidal categories, Magma code and Mathematica notebook to compute asymptotics for growth rates, related paper Asymptotics in infinite monoidal categories, joint with Abel Lacabanne and Pedro Vaz. Get the code: Click
- Orthogonal webs, Magma code and Mathematica notebook to compute related characters, related paper Orthogonal webs and semisimplification, joint with Elijah Bodish. Get the code: Click
- Weighted KLRW algebras and crystals, SageMath code for KLR algebras, related paper Cellularity of KLR and weighted KLRW algebras via crystals, joint with Andrew Mathas. Get the code: Click, Click
- Growth rates in finite monoidal categories, Magma code and Mathematica notebook to compute asymptotics for growth rates, related paper Asymptotics in finite monoidal categories, joint with Abel Lacabanne and Pedro Vaz. Get the code: Click
- Temperley-Lieb 2-representations, Mathematica notebook to compute with bilinear forms, related paper On rank one 2-representations of web categories. Get the code: Click
- Symplectic fundamental tilting characters, Mathematica notebook to compute fundamental tilting characters, related paper On a symplectic quantum Howe duality, joint with Elijah Bodish. Get the code: Click
- Symplectic differential operators, Magma code to compute symplectic differential algebras, related paper On a symplectic quantum Howe duality, joint with Elijah Bodish. Get the code: Click
- Growth rates and counting, Mathematica code to produce growth rate pictures and compute one step in the main proof, related paper Growth rates of the number of indecomposable summands in tensor powers, joint with Kevin Coulembier and Victor Ostrik. Get the code: Click
- Sandwich calculations, C++ and GAP code to compute in certain sandwich cellular algebras, related paper Sandwich cellularity and a version of cell theory. Get the code: Click
- Graded KLR(W) dimensions, Python code to compute dimensions of KLR(W) algebras, related papers Subdivision and cellularity for weighted KLRW algebras and Cellularity for weighted KLRW algebras of types BAD, joint with Andrew Mathas. Get the code: Click
- Idempotents in KLRW algebras, Tikz code to display some KLRW diagrams, related papers Subdivision and cellularity for weighted KLRW algebras and Cellularity for weighted KLRW algebras of types BAD, joint with Andrew Mathas. Get the code: Click
- Computations in monoids, Mathematica code to produce growth rate pictures, related paper Monoidal categories, representation gap and cryptography, joint with Mikhail Khovanov and Maithreya Sitaraman. Get the code: Click