Computes representation matrices for Lie groups

My undergraduate thesis in quantum computing with advisor Jamie Pommersheim. I used representation theoretic tools to analyze lower bounds of certain classes of quantum algorithms.

This thesis deals with implementation of algorithm for computation of generator of almost split sequences ending at an indecomposable nonprojective module of path algebra over finite quiver.

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

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

Handout for a seminar talk about the Hall algebra of the Jordan quiver over F1.

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

Notes on Lie algebras and their representation theory.

A web-based game to illustrate the faithfulness problem for the Burau representation of the four strand braid group

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

SAGE code for local A-packets of classical groups

Abelian unramified geometric class field theory

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 application…

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

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

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

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

On an octonionic construction of the groups of type E₆ and ²E₆

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