Mathematical research
Beauty is the first test: there is no permanent place in the world for ugly mathematics. ~ G. H. Hardy
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I am a number theorist, currently at
I am a number theorist, currently at
Carnegie Mellon University.
Carnegie Mellon University.
My CV (may be more up to date than what follows below)
Selected publications and preprints
Selected publications and preprints
On higher composition laws and reflection theorems:
Reflection theorems of Ohno-Nakagawa type for quartic rings and pairs of $n$-ary quadratic forms. Accepted at Memoirs of the AMS.
Quintic algebras over Dedekind domains and their resolvents. Research in Number Theory, Vol. 8, Paper No. 46, 2022
Reflection theorems for number rings. Ph.D. thesis, 2021.
On a remarkable identity in class numbers of cubic rings. Journal of Number Theory, 176:302–332, 2017.
Rings of small rank over a Dedekind domain and their ideals. Research in the Mathematical Sciences, 3:3:8, 2016.
On assorted topics:
Visibly irreducible polynomials over finite fields. Amer. Math. Monthly, 127(2): 112–124, 2020.
Geometry of positive configurations in affine buildings, with Ian Le. Doc. Math. 2:1519–1538, 2017.
Canonical rings of ℚ-divisors on ℙ¹. Ann. Comb., 19(4):765–784, 2015.
Continued fractions and linear fractional transformations. Integers, 15:A1, 23 pages, 2015.
Minimizing the Cayley transform of an orthogonal matrix by multiplying by signature matrices. Linear Algebra Appl., 448:97–103, 2014.
Degree asymptotics of the numerical semigroup tree. Semigroup Forum, 87(3):601–616, 2013.
Books:
The William Lowell Putnam Mathematical Competition 2001-2016: Problems, Solutions, and Commentary, with Kiran Kedlaya, Daniel Kane, and Jonathan Kane. MAA Press, 2020.
Code I've written:
Code I've written:
View my code on GitHub
If you use jEdit to edit code, you might be interested in my syntax highlighting modes for Magma and Macaulay2.
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