My research interests include arithmetic dynamics, geometry, Galois theory, and combinatorics. My publications are listed below.

**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.