My research interests include arithmetic statistics, arithmetic dynamics, geometry, Galois theory, and combinatorics.
I was awarded the Rackham Predoctoral Fellowship in the spring of 2018.
- 1. Cyclotomic factors of necklace polynomials
- 2. An acyclic arithmetic dynamical Mordell-Lang theorem
with Michael Zieve.
- 9. Liminal reciprocity and factorization statistics
to appear in Algebraic Combinatorics.
- 8. Factorization statistics and the twisted Grothendieck-Lefschetz formula,
Extended abstract. To appear in the Proceedings of 30th Conference on Formal Power Series and Algebraic Combinatorics, 2018.
- 7. Polynomial splitting measures and cohomology of the pure braid group,
with Jeffrey C. Lagarias.
The Arnold Mathematical Journal, Vol. 3, No. 2, pp. 219-249, 2017, DOI: 10.1007/s40598-017-0064-z.
- 6. Gauss' hidden menagerie: from cyclotomy to supercharacters,
with Stephan Ramon Garcia and Bob Lutz.
Notices Amer. Math. Soc., Vol. 62, No. 8, pp. 878-888, 2015.
- 5. Galois theory of the lemniscate,
with David A. Cox.
The Journal of Number Theory, Vol. 135, pp. 43-59, 2014.
- 4. Small dynamical heights for quadratic polynomials and rational functions,
with Rob Benedetto, Ruqian Chen, Yordanka Kovacheva, and Colin White.
Experimental Mathematics, Vol. 23, pp. 433-447, 2014.
- 3. A Wallis product on clovers,
The American Mathematical Monthly,
Vol. 121, No. 3, pp.237-243, 2014.
- 2. Pre-images in quadratic dynamical systems,
with Ben Hutz and Ben Krause.
Involve, Vol. 4, No. 4, pp. 343-363, 2011.
- 1. On the number of rational iterated pre-images of -1 under quadratic dynamical systems,
American Journal of Undergraduate Research,
Vol. 9, No. 1, pp. 19-26, 2010.