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<html>
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<head>
<title>mathspin - Mathematics</title>
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<h2 class="text-2xl row-span-1 place-self-center">Mathematics</h2>
<br />
<h3 class="text-xl row-span-1 place-self-center">Background</h3>
<br />
<p>
I
ranked in the top 100 in the nationwide
<a href="https://maa.org/putnam/">William Lowell Putnam Mathematical Competition®</a>, graduated from
<a href="https://www.cmu.edu/">Carnegie Mellon University</a> with an
<a href="https://en.wikipedia.org/wiki/Master_of_Science">M.S.</a> in mathematics (my thesis was on the
<a href="https://en.wikipedia.org/wiki/Modularity_theorem">modularity theorem</a>
in <a href="https://en.wikipedia.org/wiki/Number_theory">number theory</a>), and I have published research papers
on
<a href="https://en.wikipedia.org/wiki/Algebraic_number_theory">algebraic number theory</a>
and
<a href="https://en.wikipedia.org/wiki/Combinatorial_game_theory">combinatorial game theory</a>
(which applies to board games such as
<a href="https://en.wikipedia.org/wiki/Go_(game)">Go</a>).
</p>
<br />
<p>In addition, I love teaching, especially mathematics. I regularly tutor a wide variety of mathematics topics both
one-on-one and on mathematics help forums and chat servers. I also have managed and supported the creation of a
variety of online mathematics courses for the <a href="https://cty.jhu.edu/programs/online">Johns Hopkins Center for Talented Youth</a>.
</p>
<br />
<h3 class="text-xl row-span-1 place-self-center">Highlighted Publications</h3>
<br />
<ul class="row-span-1">
<li>
<details>
<summary>The positive discriminant case of Nagell's theorem for certain cubic orders</summary>
<br />
<ul class="list-disc list-outside">
<li>
Journal of Number Theory 131 (3), 470-486
</li>
<li>
It is proved that a real cubic unit <i>u</i>, whose other two conjugates are also real, is
almost always a fundamental unit of the order ℤ[<i>u</i>]. The exceptions are shown
to consist of a single infinite family together with one sporadic case. This is an analogue
of Nagell's theorem for the negative discriminant case <em>i.e.</em> the case where <i>u</i>
does not have any real conjugate.
</li>
<li>
<a href=https://www.sciencedirect.com/science/article/pii/S0022314X10002477>ScienceDirect
page</a>
</li>
</ul>
<br />
</details>
</li>
<li>
<details>
<summary>Equality Classes of Nim Positions under Misère Play</summary>
<br />
<ul class="list-disc list-outside">
<li>
INTEGERS 16, G3
</li>
<li>
We determine the misère equivalence classes of Nim positions under two equivalence
relations: one based on playing disjunctive sums with other impartial games, and one
allowing sums with partizan games. In the impartial context, the only identifications we can
make are those stemming from the known fact about adding a heap of size 1. In the partizan
context, distinct Nim positions are inequivalent.
</li>
<li>
<a href=https://math.colgate.edu/~integers/vol16.html>INTEGERS volume 16</a>
</li>
<li>
<a href=https://arxiv.org/abs/1506.02261>arXiv page</a>
</li>
</ul>
<br />
</details>
</li>
<li>
<details>
<summary>An Extension of the Normal Play Convention to <i>N</i>-player Combinatorial Games</summary>
<br />
<ul class="list-disc list-outside">
<li>
INTEGERS 20A, A14
</li>
<li>
We examine short combinatorial games for three or more players under a new play convention
in which a player who cannot move on their turn is the unique loser. We show that many
theorems of impartial and partizan two-player games under normal play have natural analogues
in this setting. For impartial games with three players, we investigate the possible
outcomes of a sum in detail, and determine the outcomes and structure of three-player Nim.
</li>
<li>
<a href=https://math.colgate.edu/~integers/vol20a.html>INTEGERS volume 20A</a>
</li>
<li>
<a href=https://arxiv.org/abs/1903.01375>arXiv page</a>
</li>
</ul>
</details>
</li>
</ul>
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