Commutative algebra and matroids

Commutative algebra, the study of rings and ideals, is one of the pillars of 20th century mathematics, playing a major role in modern geometry and algebra. Matroids appeared about 70 years ago and remain to this day important objects in discrete mathematics.
The goal of this project is to push the tools and ideas of commutative algebra into a new and exciting frontier that has opened up in the last couple of years: tropical geometry and matroid theory.

The principal project supervisor, Dr Giansiracusa, has been one of the world leaders in developing this new research direction and is at the forefront of its current development. Together, we will study the shadow of commutative algebra that remains when linear algebra is replaced by the combinatorics/discrete mathematics of matroids, developing abstract tools and computer algorithms or relevance in algebraic geometry, number theory, and possibly other areas of mathematics.

This project will require a background in pure mathematics, with strength in algebra and particularly ring theory. Graph theory would also be desirable. Knowledge of computer algebra systems such as Mathematica, SAGE, GAP, or Maple would be a plus, but is not essential.