math research (misc)

• free algebra quotient: Attempt to construct $\mathbb{C}[S_n]$ as a quotient of the noncommutative polynomial algebra $\mathbb{C}\langle x,y \rangle /I$ where $I$ is ideal of relations for symmetric group
• Fock space: Calculations involving the infinite dimensional Fock space associated to the symmetric group in Sage.
• roots of unity: Rust code to compute roots of unity in finite field, Chinese remainder theorem.
• graphs: Using the extended Cholesky decomposition, we could in principle factor any adjacency matrix $A$ as $UU^\ast$ since $A$ is symmetric.
• group preference: quantifying dynamics of a group making a decision.
• symmetric group: constructing induced repn's, restricted rep'ns, and tensor product rep'ns for SageMath
• matroids: exploring basic properties and examples of matroids which generalize the notion of linear independence
• finite general linear group: studying representations of finite groups of Lie type such as $GL_n(F_q)$
• Zipf's law: understanding rank-based ordering systems using simple Markov chain models
• elliptic curves: studying some basic properties of elliptic curves over finite fields
• finite geometry: constructs $Gr_2(F_q,r)$, the Schubert cells for the complex formed by the finite Grassmannian over $F_q$