Project description: In linear algebra, we use row echelon form to identify interesting properties of systems of linear equations, for example, the dimension or parametric form of the solution set of a system of linear equations. When we generalize these ideas beyond linear systems to arbitrary polynomial systems of equations, we arrive at the more complicated theory of Groebner bases. Subalgebra bases and Khovanskii bases are further generalizations of this concept to subalgebras of polynomial rings.

Project: The theory of subalgebra bases and Khovanskii bases has recently been established and mathematicians are starting to use these tools to study algebras. To complement this study, a software package is being developed to compute subalgebra and Khovanskii bases (along with their invariants). This software package is being written for Macaulay2, a computer algebra system. The goal of this project would be to join the welcoming team developing this software and to participate in its development.

Prerequisites:  Abstract algebra skills necessary, computer science skills are a plus.

Project faculty:
Prof. Michael Burr
Email: burr2 at clemson.edu (change "at" to "@")
Office hours: TBA
Bio: coming soon