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<!DOCTYPE html>
<html lang="en-US">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<meta name="description" content="Travis Scrimshaw's research and interests">
<meta name="author" content="Travis Scrimshaw">
<meta name="keywords" content="Travis Scrimshaw, Mathematics, Combinatorics, Representation Theory, Hokkaido University">
<! -- Mathjax -->
<script type="text/javascript" async
src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<link rel="stylesheet" href="main.css">
<title>Travis Scrimshaw's Homepage</title>
</head>
<body id="home">
<header>
<h1>Travis Scrimshaw's Homepage</h1>
</header>
<nav>
<ul>
<li><a class="active" href="#home">Home</a></li>
<li><a href="research.html">Research</a></li>
<li><a href="publications.html">Publications</a></li>
<li style="float:right" class="dropdown">
<a href="javascript:void(0)" class="dropbtn">Links</a>
<div class="dropdown-content">
<a href="https://arxiv.org/">arXiv</a>
<a href="http://www.sagemath.org/">SageMath</a>
<a href="http://www.findstat.org/">FindStat</a>
<a href="https://oeis.org/">OEIS</a>
</div>
</li>
<li style="float:right">
<a href="https://scholar.google.com/citations?hl=en&user=5-M3BPAAAAAJ">
<img alt="Google scholar" src="scholar_24x24.png"
width="24" height="24" style="position:relative;bottom:-2px;"/></a>
</li>
<li style="float:right">
<a href="https://orcid.org/0000-0003-0326-4442">
<img alt="ORCID" src="orcid_24x24.png"
width="24" height="24" style="position:relative;bottom:-2px;"/></a>
</li>
<li style="float:right">
<a href="https://arxiv.org/a/scrimshaw_t_1.html">
<img alt="arXiv" src="arxiv-logomark-small.svg"
width="24" height="24" style="position:relative;bottom:-2px;"/></a>
</li>
</ul>
</aside> <!-- links -->
</nav>
<main>
<article>
<section id="about">
<h2>About me</h2>
<!-- <img src="himeji.jpg" alt="Me in Himeji" style="padding-left:20px;float:right;width:450px;height:300px;"> -->
<img src="myphoto.jpg" alt="My photo" style="padding-left:20px;float:right;width:300px;height:300px;">
<p>
I am currently an associate professor (准教授) at <a href="https://www.global.hokudai.ac.jp/">Hokkaido University</a>
(<a href="https://www.hokudai.ac.jp/">北海道大学</a>)
in the <a href="https://www2.sci.hokudai.ac.jp/dept/math/en">Department of Mathematics<a/>
(<a href="https://www2.sci.hokudai.ac.jp/dept/math/">数学部門</a>)
within the <a href="https://www2.sci.hokudai.ac.jp/faculty/en">Faculty of Science</a>
(<a href="https://www2.sci.hokudai.ac.jp/faculty/">大学院理学研究院</a>).
I received my Ph.D. in Mathematics from
<a href="https://www.ucdavis.edu/">University of California, Davis</a> in 2015
under the guidance of <a href="https://www.math.ucdavis.edu/~anne/">Anne Schilling</a>.
From 2015 to 2017, I was an RTG Postdoctoral Associate as part of the
combinatorics group at the <a href="http://www.umn.edu/">University of Minnesota</a>,
specifically under the mentorship of
<a href="https://sites.google.com/site/pylyavskyy/">Pavlo Pylyavskyy</a>.
From 2017 to 2019, I was a Postdoctoral Research Fellow at
<a href="http://www.uq.edu.au/">The University of Queensland</a> under the
mentorship of <a href="https://people.smp.uq.edu.au/OleWarnaar/">Ole Warnaar</a>.
From 2019 to 2021, I was a lecturer at
<a href="http://www.uq.edu.au/">The University of Queensland</a>.
From 2021 to 2022, I was a JSPS Standard Postdoc located at
<a href="http://www.sci.osaka-cu.ac.jp/OCAMI/index_e.html">OCAMI</a>
(<a href="http://www.sci.osaka-cu.ac.jp/OCAMI/">数学研究所<a>) within
<a href="https://www.upc-osaka.ac.jp/new-univ/en-research/">Osaka Metropolitan University</a>
(<a href="https://www.omu.ac.jp/">大阪公立大学</a>)
and hosted by
<a href="http://www.sci.osaka-cu.ac.jp/~okado/index-e.html">Masato Okado</a>.
</p>
</section>
<section id="research">
<h2>Research</h2>
<p>
My primary research interests are in combinatorics and representation theory,
specifically in the area of crystals and (Kac–Moody) Lie algebras.
My research focuses on a specific class of finite crystals for affine Lie
algebras called <em>Kirillov–Reshetikhin (KR) crystals</em> and
combinatorial objects called rigged configurations.
The (conjectural) bijection between tensor products of KR crystals and
rigged configurations of objects arose from statistical mechanics and has
led to applications in soliton cellular automata, a generalization of the
box-ball system. In particular, this would give a (combinatorial) proof of
the \(X = M\) conjecture. Characters of tensor products of KR crystals also
have deep connections with other areas of mathematics, including
<a href="https://en.wikipedia.org/wiki/Macdonald_polynomials">(non)symmetric Macdonald polynomials<a/>
and Q-systems. <a href="http://people.cst.cmich.edu/salis1bt/">Ben Salisbury</a>
and I have also generalized rigged configurations to be a model for highest
weight crystals, where they appear to be a very natural model.
</p>
<p>
Additionally, I am interested in generalizations of crystals; specifically
in geometric crystals, a rational lifting of crystals, and crystals for
Lie superalgebras and Borcherds algebras. Recently I have been working on
developing a theory of crystals related to the K-theory of the Grassmannian
and Schubert calculus and with stochastic processes. I have additional
interests in combinatorial Hopf algebras, which includes symmetric functions,
Coxeter and Artin groups, and Hecke algebras.
</p>
<p>
For more information, see my <a href="research.html">research page</a>.
Here is my <a href="publications.html">publication list</a>.
<ul>
<li>
<a href="https://arxiv.org/"><img alt="arXiv logo" src="arxiv-logo.svg"
width="60" style="position:relative;bottom:-8px;"/></a>
<a href="https://arxiv.org/a/scrimshaw_t_1.html">my arXiv papers</a>
</li>
<li>
ORCID
<a href="http://orcid.org/"><img alt="ORCID logo" src="orcid_24x24.png"
width="24" height="24" style="position:relative;bottom:-6px;"/></a>
<a href="https://orcid.org/0000-0003-0326-4442">https://orcid.org/0000-0003-0326-4442</a>
</li>
<li>
<a href="https://scholar.google.com"><img alt="Google scholar logo" src="scholar_24x24.png"
width="24" height="24" style="position:relative;bottom:-6px;"/></a>
<a href="https://scholar.google.com/citations?hl=en&user=5-M3BPAAAAAJ">
Google scholar</a>
</li>
<li>
<a href="https://researchmap.jp/tscrim">Researchmap</a>
</li>
<li>
J-Global ID:
<a href="https://jglobal.jst.go.jp/en/detail?JGLOBAL_ID=202201002897414434">202201002897414434</a>
</li>
<li>
<a href="https://www2.sci.hokudai.ac.jp/dept/math/en/researcher/scrimshaw-travis-2">Department of Mathematics webpage</a>
(<a href="https://www2.sci.hokudai.ac.jp/dept/math/researcher/scrimshaw-travis">日本語</a>)
</li>
<li>
<a href="https://researchers.general.hokudai.ac.jp/profile/en.6a78ca4de758b40d520e17560c007669.html">Hokkaido University webpage</a>
(<a href="https://researchers.general.hokudai.ac.jp/profile/ja.6a78ca4de758b40d520e17560c007669.html">日本語</a>)
</li>
</ul>
</p>
</section> <!-- research -->
<section id="outreach">
<h2>Other stuff</h2>
<p>
I am co-organizing <a href="https://fpsac.org/confs/fpsac-2025/">FPSAC 2025</a>
with Kyouko Kimura, Nanao Kita, Tomoo Matsumura, and Yasuhide Numata.
</p>
<p>
I am co-organizing the <a href="pacs_en.html">PACSeminar</a>
(<a href="pacs.html">日本語</a>) with Hideya Watanabe.
</p>
<p>
I have been a developer for the open-source mathematical software
<a href="https://www.sagemath.org">SageMath</a> since 2010 and have been
programming in various languages (C, C++, C#, Java, Python, etc.) since 2001.
For books on SageMath, see
<a href="http://sagebook.gforge.inria.fr/english.html">Computational mathematics with SageMath</a>
(also available from a <a href="http://bookstore.siam.org/ot160/">traditional publisher</a>) and <a href="http://www.gregorybard.com/Sage.html">Gregory Bard's book</a>.
</p>
</section> <!-- outreach -->
</article>
</main>
<hr/>
<footer>
<p>Contact: tcscrims {at} gmail.com, scrimshaw {at} oia.hokudai.ac.jp</p>
</footer>
</body>
</html>