My research interests include arithmetic statistics, arithmetic dynamics, geometry of configuration spaces, Galois theory, and algebraic combinatorics.
In 2020 I received the NSF Mathematical Sciences Postdoctoral Research Fellowship.
In May of 2019 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.
Preprints
Publications
 Cyclotomic factors of necklace polynomials,
To appear in Acta Arithmetica,
arXiv preprint 1811.08601.
 Dynatomic polynomials, necklace operators, and universal relations for dynamical units,
with John R. Doyle and Paul Fili,
To appear in New York Journal of Mathematics,
arXiv preprint 2108.09333.
 Dynamical moduli spaces and polynomial endomorphisms of configurations,
with Talia Blum, John R. Doyle, Colby Kelln, Henry Talbott, and Max Weinreich,
Arnold Mathematical Journal, 2022, DOI: 10.1007/s4059802200197z
 Euler characteristic of the sp
ace of real multivariate irreducible polynomials,
Proceedings of the AMS, Vol. 150, 2022, 23312343.
 Density of periodic points for Lattès maps over finite fields,
with Zoë Bell, Jasmine Camero, Karina Cho, ChiehMi Lu, Rebecca Miller, Bianca Thompson, and Eric Zhu,
Journal of Number Theory, 2021, DOI:10.1016/j.jnt.2021.10.009
 Polynomial factorization statistics and point configurations in R^3,
International Mathematical Research Notices, 2018, DOI: 10.1093/imrn/rny271.
 Liminal reciprocity and factorization statistics,
Algebraic Combinatorics, Vol. 2, No. 4, 2019, 521539.
 Factorization statistics and the twisted GrothendieckLefschetz formula,
extended abstract, Proceedings of 30th Conference on Formal Power Series and Algebraic Combinatorics, 2018.
 Polynomial splitting measures and cohomology of the pure braid group,
with Jeffrey C. Lagarias.
Arnold Mathematical Journal, Vol. 3, No. 2, 2017, 219249, DOI: 10.1007/s405980170064z.
 Gauss' hidden menagerie: from cyclotomy to supercharacters,
with Stephan Ramon Garcia and Bob Lutz.
Notices Amer. Math. Soc., Vol. 62, No. 8, 2015, 878888.
 Galois theory of the lemniscate,
with David A. Cox.
The Journal of Number Theory, Vol. 135, 2014, 4359.
 Small dynamical heights for quadratic polynomials and rational functions,
with Rob Benedetto, Ruqian Chen, Yordanka Kovacheva, and Colin White.
Experimental Mathematics, Vol. 23, 2014, 433447.
 A Wallis product on clovers,
The American Mathematical Monthly, Vol. 121, No. 3, 2014, 237243.
 Preimages in quadratic dynamical systems,
with Ben Hutz and Ben Krause.
Involve, Vol. 4, No. 4, 2011, 343363.
 On the number of rational iterated preimages of 1 under quadratic dynamical systems,
American Journal of Undergraduate Research, Vol. 9, No. 1, 2010, 1926.
Doctoral Thesis
Invited Talks

Arithmetic Dynamics International Online Seminar (ADIOS),
February, 2022.

Algebraic Dynamics Seminar,
Harvard University, February, 2022.

Number Theory Seminar,
Oklahoma State University, March, 2021.
Video

Algebraic Geometry Seminar,
University of Washington, February, 2021.

Math Club,
University of Connecticut, October, 2020.

Arithmetic Dynamics Special Session,
Joint Math Meetings, January, 2020.

Combinatorial and Additive Number Theory Workshop,
CUNY Graduate Center, May, 2019.

Midwest Representation Stability Research Meeting,
University of Chicago, April, 2019.

Emerging Connections in Number Theory,
AMS Sectional Meeting, March, 2019.

Graduate Recruitment Symposium,
University of Michigan, March, 2019.

Michigan Complex Analysis, Dynamics, and Geometry Seminar,
University of Michigan, March, 2019.

Michigan Combinatorics Seminar,
University of Michigan, February, 2019.

Wayne State Algebra Seminar,
Wayne State University, January, 2019.

Berkeley Combinatorics Seminar,
University of California, November, 2018.

University of Chicago Geometry/Topology Seminar,
University of Chicago, November, 2018.

Formal Power Series and Algebraic Combinatorics,
Dartmouth College, July, 2018.

Combinatorial and Additive Number Theory Workshop,
CUNY Graduate Center, May, 2018.

Arithmetic Dynamics Special Session,
AMS Sectional Meeting, Northeastern University, April, 2018.

Arithmetic Dynamics Special Session,
Joint Math Meetings, January, 2018.

Workshop on Interactions between Model Theory and Arithmetic Dynamics,
Fields Institute, July, 2016.

Colloquium,
Amherst College, April, 2013.

Pi Day Colloquium,
University of Connecticut, Mansfield, March, 2013.