Main development repository for GAP - Groups, Algorithms, Programming, a System for Computational Discrete Algebra

Tools for exploiting Morphological Symmetries in robotics

On-the-fly generator of space-group irreducible representations

Official PyTorch implementation of Bispectral Neural Networks, ICLR 2023

Isomorphisms of quiver representations applied to neural networks.

Interactive exploration of equivariant neural networks on homogeneous spaces, with a focus on the sphere S² as SO(3)/SO(2). From Lecture 8 of the Lie groups course with Quantum Formalism

many powerful tools for studying irreducible representations of SU(n), including making animations of hadron flavor-state multiplets

A computer algebra system in Smalltalk

Decompose representations of finite groups into irreducibles

Notes for the lecture course “Foundations in Representation Theory”.

MLOne Powered by AIEdX. Machine Learning Course for Everyone. Tier1 Basic

AIDN is a deep learning algorithm to represent any finitely-presented algebraic object with a set of deep neural networks.

Code to run the experiments of the Neurips 2022 paper On the Symmetries of Deep Learning Models and their Internal Representations.

Geometric algebra crate for Rust

Computes representation matrices for Lie groups

Mathematically sound structures and fast algorithms for things around representation theory, especially algebraic Lie theory and accompanying combinatorics.

SageMath code for moduli space invariants

Computes the generators for a given representation of SU2 and SU3.

Notes on Lie algebras and their representation theory.

A research-oriented multiplayer battle game where you train AI agents to compete in a zombie-infested arena!

Miscellaneous math research calculations in various languages.

In this project, we attempt to reformulate various notions from classical commutative algebra (such as flatness, regularity, smoothness, etc.) in an entirely categorical manner, so as to be able to later write down their analogues in derived algebraic geometry without having to develop extra theory. We will also be presenting certain applications, such as deformation theory, the theory of D-modules, and certain motivic/geometric aspects of p-adic Hodge theory.

QSym² - a Rust program for Quantum Symbolic Symmetry. This is only a mirror. Please visit the main repository on GitLab. Documentation at https://qsym2.dev.

Drafts of textbooks. One on the math inspired by supersymmetric field theories. One on low dimensional (below 3+1) integrable physics.

Search for non-trivial elements of the kernel of the Burau representation of the four-strand braid group.

Linear-time sequence modeling that replaces attention's O(n²d) complexity with O(nd) summation-based aggregation. Demonstrates constraint-driven emergence: how functional representations can develop from optimization pressure and architectural constraints alone, without explicit pairwise interactions.

Handout for a seminar talk about the quantum group U_q(sl2).

Notes about "An introduction to Finite Group Representation Theory using Agda"

An interactive exploration of the representation theory of the Lie algebra sl(2,C), as part of lecture 4 of Quantum Formalism's course on Lie groups with applications.

A Mathematica package for studies and applications of the Brauer Algebra