# Research

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] - 'Lattice paths and submonoids of $\mathbb{Z}^2$' (with James East)

[Annals of Combinatorics, arXiv]

#### Unpublished Papers

- 'Notions of Symmetry for Finite Strategic-Form Games'

[arXiv, arXiv v1] [recent drafts - GitLab, pdf]

#### Unfinished Papers

- 'Lattice path conjectures'

[recent drafts - GitLab, pdf] - 'Exploring Euclid's Orchard'

[recent drafts - pdf]

(also James East typesetted his approach for the Density of Euclid's Orchard)

#### 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

- 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
- Organised a weekly algebra seminar at the University of Tasmania from 2012-2014.