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.

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 F_2[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. Sawheny 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 one. (with J. Specter). International Mathematics Research Notices IMRN. (2015), no. 24, 13047-13061.
Congruences for Ramanujan's f and ω functions via generalized Borcherds products. (with J. Berg, A. Castillo, R. Grizzard, V. Kala, and C. Wang). 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.