Research
I am primarily interested in algebraic number theory and arithmetic statistics. In particular, I am interested in studying the shapes of number fields, unit lattices, and in the asymptotics of number fields. If you are interested in hearing more about these projects, or talking about other projects, send me an email!
I have also had the opportunity to work on a few fun projects in arithmetic dynamics, algebraic geometry, and a biologically inspired project involving permutation groups and game theory.
Preprints/Projects
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Shapes of sextic fields and log-terms in Malle's conjecture
(with Rob Harron)
(in preparation)
I gave a talk about this work at the JMM: you can find the abstract here.
-
On local algebras and the genus theory of S_n number fields
(with Ben Breen
and
Angelica Babei)
(in progress)
-
Shapes of unit lattices: Ongoing project dedicated to unit lattices and their shapes. The first paper of this project is in preparation.
Papers
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Adelic perturbation of rational functions and applications with Félix Baril Boudreau and Khoa Nguyen. (Submitted)
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On the shapes of pure prime degree number fields (Submitted)
(Extends the equidistribution results of my dissertation to all primes)
- (Dissertation)
Shapes of pure prime degree number fields.
ProQuest Dissertations Publishing, 2021. 28718070.
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Sorting permutations: Games, Genomes and Cycles
(with
K.L.M. Adamyk,
G. Mayfield,
D.J. Moritz,
M. Scheepers,
B.E. Tenner and
H.C. Wauck)
Discrete Mathematics, Algorithms and Applications 9:5 (2017), 1750063 (31 pp)
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Maximum Waring ranks of monomials
(with
Paul Plummer,
Jeremy Siegert,
Zach Teitler)
Comm. Alg. 44 (2016), no. 10, 4212--4219
Other writing