Research

I am in the final year of my PhD, having begun in late 2014. I am supervised by Dr James D. Mitchell, a Reader at the School of Mathematics and Statistics.

The topic of my PhD is semigroup theory. During the course of my studies, I hope to advance the state of the art of computational semigroup theory, both in a theoretical way, and in practice by implementing new results in the Semigroups package for GAP. More information about my software contributions is detailed on the software page of this website.

Collaborators

I have worked closely with the following mathematicians:


Publications

  1. "Maximal subsemigroups of finite transformation and diagram monoids",
    with James East, Jitender Kumar, and James D. Mitchell,
    to appear in Journal of Algebra, arxiv.org/abs/1706.04967.
  2. "Computing maximal subsemigroups of a finite semigroup",
    with C. R. Donoven and J. D. Mitchell,
    to appear in Journal of Algebra, arxiv.org/abs/1606.05583.

Undergraduate research

I first became involved in mathematics research as an undergraduate. In the summers after my second and third years, I received a Vacation Scholarship from the Carnegie Trust to undertake research in pure mathematics. Some highlights of my undergraduate research include:

2012: Inverse semigroups

I was part of a team who contributed new functions to the Semigroups package for inverse semigroups. Most significantly, we implemented the function SmallerDegreePartialPermRepresentation, which reduces the degree of an inverse semigroup of partial permutations.

2013: Maximal subsemigroups

In 2013, I began working with James Mitchell, Casey Donoven, and others to solve the problem of computing the maximal subsemigroups of an arbitrary finite semigroup. This research turned out to be surprisingly tricky, and it became the basis for the final year project of my undergraduate degree (PDF). The functions that we created as a result of this research are available in the Semigroups package.