Research

My research interests mostly lie in the area of algebraic number theory with particular interest in understanding and computing Hilbert modular forms. I also have interests in various areas of discrete mathematics.

Publications:

The papers below may be found on the arXiv or Google Scholar.

Finite abelian groups with toroidal subgroup lattices. Submitted.
Monodromy groups of dessins d’enfant on rational polygonal billiards surfaces (with J. Schmurr and J. Varlack). Accepted in Rocky Mountain Journal of Mathematics.
Monodromy groups of dessins d’enfant on rational triangular billiards surfaces. (with M. Mabe, J. Schmurr, and J. Varlack) Involve 16 (2023), no. 1, 49–58.
The distance to a squarefree polynomial over 𝔽₂[x]. (with M. Filaseta) Acta Arithmetica 193 (2020), no. 4, 419–427.
Shabat polynomials and monodromy groups of trees uniquely determined by their passport.
(with N. Cameron, M. Kemp, S. Maslak, G. Melamed, J. Pham, and A. Wei) Involve 12 (2019), no. 5, 791–812.
Stanley sequences with odd character.
Journal of Combinatorics 9 (2018), no. 4, 599–618.
On the Galois group over ℚ of a truncated binomial expansion.
(with M. Filaseta) Colloquium Mathematicum 154 (2018), no. 2, 295–308.
Characters of independent Stanley sequences.
(with M. Sawhney and D. Stoner) European Journal of Combinatorics 70 (2018), 354–363.
Novel structures in Stanley sequences.
(with D. Rolnick) Discrete Mathematics 339 (2016), no. 2, 689–698.
There exist non-CM Hilbert modular forms of partial weight 1.
(with J. Specter) International Mathematics Research Notices (2015), no. 24, 13047–13061.
Congruences for Ramanujan’s ƒ and ω functions via generalized Borcherds products.
(with J. Berg, A. Castillo, R. Grizzard, V. Kala, and C. Wang) The Ramanujan Journal 35 (2014), no. 2, 327–338.
Congruences among power series coefficients of modular forms.
International Journal of Number Theory 9 (2013), no. 6, 1447–1474.
On the growth of the counting function of Stanley sequences.
Discrete Mathematics 311 (2011), no. 7, 560–562.