My research interests include arithmetic dynamics, geometry, Galois theory, and combinatorics. My publications are listed below.
- Factorization statistics and the twisted Grothendieck-Lefschetz formula,
Extended abstract submitted for consideration in the 2018 FPSAC.
- Collusions in Teichmüller expansions
- Circulant q-Butson Hadamard matrices,
with Joe Kraisler.
- Polynomial splitting measures and cohomology of the pure braid group,
with Jeffrey C. Lagarias.
To appear in The Arnold Mathematical Journal. DOI: 10.1007/s40598-017-0064-z.
- 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.
- Galois theory of the lemniscate,
with David A. Cox.
The Journal of Number Theory, Vol. 135, pp. 43-59, 2014.
- 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.
- A Wallis product on clovers,
The American Mathematical Monthly,
Vol. 121, No. 3, pp.237-243, 2014.
- Pre-images in quadratic dynamical systems,
with Ben Hutz and Ben Krause.
Involve, Vol. 4, No. 4, pp. 343-363, 2011.
- 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.