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<!doctype html><html lang="en"><head><title>n-ham</title> <meta charset="utf-8"><meta name="viewport"content="width=device-width, initial-scale=1"><meta name="description"content="personal site of nicholas ham"><link rel="stylesheet"href="assets/css/style.css"><link rel="icon"type="image/png"href="assets/images/favicon.png"media="print"onload="this.media='all'"></head> <body><div align="center"id="body"><div class="menu-bars"><i id="open-menu-icon"class="fa fa-bars-png fa-rnbw"onclick="show_menu()"></i></div> <div id="menu-page"><div class="menu-cross"><i id="close-menu-icon"class="fa fa-xmark-png fa-rnbw"onclick="close_menu()"></i></div> <nav id="nav"class="noselect"><ul><li class="item li-menu li-dark"><a class="item-link"href="index.html">home</a></li> <li class="item li-menu li-dark has-submenu"><a tabindex="0"href="#"class="submenu-link"onclick="toggle_submenu(0)">work<i class="submenu-link-icon fa fa-angle-down-png fa-1x"></i></a> <ul class="submenu"align="center"><li class="subitem"><a href="programming.html">programming</a></li> <li class="subitem"><a href="research.html">research</a></li> <li class="subitem"><a href="education.html">education</a></li> <li class="subitem"><a href="teaching.html">teaching</a></li> <li class="subitem"><a href="genealogy.html">genealogy</a></li> <li class="subitem"><a href="links.html">links</a></li></ul></li> <li class="item li-menu li-dark has-submenu"><a tabindex="0"href="#"class="submenu-link"onclick="toggle_submenu(1)">play<i class="submenu-link-icon fa fa-angle-down-png fa-1x"></i></a> <ul class="submenu"><li class="subitem"><a href="generative_art.html">art</a></li> <li class="subitem"><a href="nature.html">nature</a></li> <li class="subitem"><a href="skateboarding.html">skateboarding</a></li></ul></li></ul></nav></div> <div id="content"><h1>Research</h1> <p>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.</p> <h4>Theses</h4> <ul><li>'The Planar Modular Partition Monoid', PhD Thesis, 2015, Supervisors: Des FitzGerald and Peter Jarvis <br>[<a href="https://eprints.utas.edu.au/23029/">eprints</a>, <a href="https://arxiv.org/abs/1808.07156">arXiv</a>]</li> <li>'Some Structure Properties of Finite Normal-Form Games', Honours Thesis, 2011, Supervisor: Des FitzGerald <br>[<a href="https://arxiv.org/abs/1905.00636">arXiv</a>, <a href="https://gitlab.com/n-ham-papers/honours-thesis/">GitLab</a>, <a href="pdfs/Some_Structure_Properties_of_Finite_Normal-Form_Games.pdf">pdf</a>]</li></ul> <h4>Published Papers</h4> <ul><li>'Enumeration of idempotents in planar diagram monoids' (with Igor Dolinka, James East, Athanasios Evangelou, Des FitzGerald, James Hyde, Nicholas Loughlin, James Mitchell) <br>[<a href="https://www.sciencedirect.com/science/article/pii/S0021869318306550">Journal of Algebra</a>, <a href="https://arxiv.org/abs/1507.04838">arXiv</a>]</li> <li>'Enumeration of idempotents in diagram semigroups and algebras' (with Igor Dolinka, James East, Athanasios Evangelou, Des FitzGerald, James Hyde, Nicholas Loughlin) <br>[<a href="https://www.sciencedirect.com/science/article/pii/S0097316514001563">Journal of Combinatorial Theory, Series A</a>, <a href="https://arxiv.org/abs/1408.2021">arXiv</a>]</li> <li>'Lattice paths and submonoids of $\mathbb{Z}^2$' (with James East) <br>[<a href="https://link.springer.com/article/10.1007/s00026-021-00546-3">Annals of Combinatorics</a>, <a href="https://arxiv.org/abs/1811.05735">arXiv</a>]</li></ul> <h4>Unpublished Papers</h4> <ul><li>'Notions of Symmetry for Finite Strategic-Form Games' <br>[<a href="https://arxiv.org/abs/1311.4766">arXiv</a>, <a href="https://arxiv.org/abs/1311.4766v1">arXiv v1</a>] [recent drafts - <a href="https://gitlab.com/n-ham-paper-drafts/symmetry-notions-for-finite-strategic-form-games">GitLab</a>, <a href="pdfs/Notions of Anonymity, Fairness and Symmetry for Finite Strategic-Form Games.pdf">pdf</a>]</li></ul> <h4>Unfinished Papers</h4> <ul><li>'Lattice path conjectures' <br>[recent drafts - <a href="https://gitlab.com/n-ham-paper-drafts/lattice-path-conjectures">GitLab</a>, <a href="pdfs/Lattice Path Conjectures.pdf">pdf</a>]</li> <li>'Exploring Euclid's Orchard' <br>[recent drafts - <a href="pdfs/Exploring Euclid's Orchard.pdf">pdf</a>] <br>(also James East typesetted his approach for the <a href="pdfs/EO - authored by James East.pdf">Density of Euclid's Orchard</a>)</li></ul> <h4>Acknowledgements</h4> <ul><li>'Fiscal and Monetary Policy in Australia: an SVAR Model*' (Mardi Dungey, Renée Fry) <br>[<a href="https://www.researchgate.net/profile/Mardi_Dungey/publication/228433588_Fiscal_and_Monetary_Policy_in_Australia_an_SVAR_Model/links/551184730cf20bfdad4e7621/Fiscal-and-Monetary-Policy-in-Australia-an-SVAR-Model.pdf">ResearchGate</a>]</li> <li>'GAP Package Semigroups' <br>[<a href="https://semigroups.github.io/Semigroups/">GitHub</a>]</li></ul> <h4>Conference Talks</h4> <ul><li>'The mod-$m$ diagram monoids' - 33rd Annual Victorian Algebra Conference, 4th Annual Australian Mathematical Sciences Student Conference <br>[<a href="pdfs/nchamVAC33.pdf">slides</a>]</li> <li>'The Fauser Monoid' - 32nd Annual Victorian Algebra Conference, 58th Annual AustMS Meeting <br>[<a href="pdfs/nchamFauser14.pdf">slides</a>]</li> <li>'Classifications of Symmetric Normal Form Games' - 31st Annual Victorian Algebra Conference, 57th Annual AustMS Meeting <br>[<a href="pdfs/nchamVAC31.pdf">slides</a>]</li></ul> <h4>OEIS Contributions</h4> <p>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: <ul><li><a href="https://oeis.org/A005043">A005043</a></li> <li><a href="https://oeis.org/A005165">A005165</a></li> <li><a href="https://oeis.org/A035343">A035343</a></li> <li><a href="https://oeis.org/A067955">A067955</a></li> <li><a href="https://oeis.org/A097609">A097609</a></li> <li><a href="https://oeis.org/A308087">A308087</a></li></ul></p> <h4>Organised Seminars & Conferences</h4> <ul><li>Treasurer of the <a href="https://www.amssc.org/2015/">4th Annual Australian Mathematical Sciences Student Conference</a>, held at the University of Tasmania from the 30th November until the 2nd of December 2015</li> <li>Organised a weekly algebra seminar at the University of Tasmania from 2012-2014.</li></ul> <div id="footer"align="center"><br><hr><br><div class="noselect"><a href="https://github.com/n-ham"title="GitHub"><i class="fa fa-github-png fa-rnbw"></i></a> <a href="mailto:[email protected]"title="Email"><i class="fa fa-envelope-png fa-rnbw"></i></a> <a href="https://orcid.org/0000-0002-4984-1711"title="ORCID"><i class="fa fa-orcid-png fa-rnbw"></i></a> <a href="https://scholar.google.com/citations?user=vV-pxo4AAAAJ&hl=en"title="Google Scholar"><i class="fa fa-google-png fa-rnbw"></i></a> <a href="https://arxiv.org/a/ham_n_2.html"title="arXiv"><i class="fa fa-box-archive-png fa-rnbw"></i></a></div> <p><b>Mirrors:</b> [<a href="https://n-ham.com/">Official</a>] [<a href="https://n-ham.bitbucket.io/">BitBucket</a>] [<a href="https://n-ham.github.io/">GitHub</a>] [<a href="https://n-ham.gitlab.io/">GitLab</a>]</p> <p><b>Source:</b> [<a href="https://github.com/n-ham/n-ham.github.io/">GitHub</a>]</p> <p>Page was last built using <a href="https://nift.dev">Nift</a> on Friday May 05 2023 at 07:45:41 (AEST).</p> <picture alt="tassie devil"><source media="(max-width: 750px)"srcset="assets/images/w=500px/devil-toon.webp"><source srcset="assets/images/devil-toon.webp"><img src="assets/images/devil-toon.webp"alt="tassie devil"loading="lazy"height=200 width=300></picture></div></div></div> <script type="text/javascript"src="assets/js/bundle.js"></script></body></html>