Research

Research Interests

My main research interests are diagram semigroups and algebras, along with notions of symmetry for finite strategic-form games, though I typically find most problems under the very broad umbrellas of algebra and combinatorics interesting.

Theses

  • 'The Planar Modular Partition Monoid', PhD Thesis, 2015, Supervisors: Des FitzGerald and Peter Jarvis
    [eprints, arXiv]
  • 'Some Structure Properties of Finite Normal-Form Games', Honours Thesis, 2011, Supervisor: Des FitzGerald
    [arXiv, GitLab, pdf]

Published Papers

  • 'Enumeration of idempotents in planar diagram monoids' (with Igor Dolinka, James East, Athanasios Evangelou, Des FitzGerald, James Hyde, Nicholas Loughlin, James Mitchell)
    [Journal of Algebra, arXiv]
  • 'Enumeration of idempotents in diagram semigroups and algebras' (with Igor Dolinka, James East, Athanasios Evangelou, Des FitzGerald, James Hyde, Nicholas Loughlin)
    [Journal of Combinatorial Theory, Series A, arXiv]

Unpublished Papers

  • 'Lattice paths and submonoids of $\mathbb{Z}^2$' (with James East)
    [arXiv]
  • 'Notions of Symmetry for Finite Strategic-Form Games'
    [arXiv, arXiv v1] [recent drafts - GitLab, pdf]

Working Papers

  • 'Lattice path conjectures'
    [recent drafts - GitLab, pdf]

Acknowledgements

  • 'Fiscal and Monetary Policy in Australia: an SVAR Model*' (Mardi Dungey, RenĂ©e Fry)
    [ResearchGate]
  • 'GAP Package Semigroups'
    [GitHub]

Conference Talks

  • 'The mod-$m$ diagram monoids' - 33rd Annual Victorian Algebra Conference, 4th Annual Australian Mathematical Sciences Student Conference
    [slides]
  • 'The Fauser Monoid' - 32nd Annual Victorian Algebra Conference, 58th Annual AustMS Meeting
    [slides]
  • 'Classifications of Symmetric Normal Form Games' - 31st Annual Victorian Algebra Conference, 57th Annual AustMS Meeting
    [slides]

OEIS Contributions

The On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences. It was created and maintained by Neil Sloane while a researcher at AT&T Labs. Some of the integer sequences that I have made contributions to are:

Organised Seminars & Conferences

  • I was treasurer of the 4th Annual Australian Mathematical Sciences Student Conference, held at the University of Tasmania from the 30th November until the 2nd of December 2015
  • From 2012-2014 I organised the $G$-seminar weekly at the University of Tasmania. Primarily talks had an algebraic flavour, with the name playfully hinting towards a common theme of objects containing $G$ such as Groups, semiGroups, Games and Gombinatorics