My research interests include arithmetic statistics, arithmetic dynamics, geometry, Galois theory, and combinatorics.
In November of 2018 I received the Wirt and Mary Cornwell Prize in mathematics from the University of Michigan.
I received the Rackham Predoctoral Fellowship in the spring of 2018.
- 1. An acyclic arithmetic dynamical Mordell-Lang theorem
with Michael Zieve.
- 10. Polynomial factorization statistics and point configurations in R^3,
International Mathematical Research Notices, 2018.
- 9. Liminal reciprocity and factorization statistics,
to appear in Algebraic Combinatorics, 2018.
- 8. Factorization statistics and the twisted Grothendieck-Lefschetz formula,
extended abstract, 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.
12. Michigan Complex Analysis, Dynamics, and Geometry Seminar,
University of Michigan, March, 2019.
11. Michigan Combinatorics Seminar,
University of Michigan, February, 2019.
10. Wayne State Algebra Seminar,
Wayne State University, January, 2019.
9. Berkeley Combinatorics Seminar,
University of California, November, 2018.
8. University of Chicago Geometry/Topology Seminar,
University of Chicago, November, 2018.
7. Formal Power Series and Algebraic Combinatorics,
Dartmouth College, July, 2018.
6. Combinatorial and Additive Number Theory Workshop,
CUNY Graduate Center, May, 2018.
5. AMS Sectional Meeting,
Arithmetic Dynamics Special Session, Northeastern University, April, 2018.
4. Joint Math Meetings,
Arithmetic Dynamics Special Session, January, 2018.
3. Interactions between Model Theory and Arithmetic Dynamics,
Fields Institute, July, 2016.
Amherst College, April, 2013.
1. Pi Day Colloquium,
University of Connecticut, Mansfield, March, 2013.