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.

- 1.
**Normal elements in finite fields**,

arXiv preprint 1809.02155. - 2.
**Polynomial factorization statistics and point configurations in R^3**,

arXiv preprint 1802.00305. - 3.
**An arithmetic dynamcial Mordell-Lang theorem**

with Michael Zieve.*Submitted.* - 4.
**Reduction stability and iterate decomposition stability**

with Michael Zieve.*Submitted.*

- 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.