My research interests include arithmetic statistics, arithmetic dynamics, geometry, Galois theory, and combinatorics.
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.
Doctoral Thesis
Preprints
Publications
- 10. Polynomial factorization statistics and point configurations in R^3,
International Mathematical Research Notices, 2018, DOI: 10.1093/imrn/rny271.
- 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.
Invited Talks
-
17. Garsiafest: New Directions in Algebraic Combinatorics,
90th birthday conference for Prof. Adriano Garsia,
Scripps Seaside Forum, June, 2019.
-
16. Combinatorial and Additive Number Theory Workshop,
CUNY Graduate Center, May, 2019.
-
15. Midwest Representation Stability Research Meeting,
University of Chicago, April, 2019.
-
14. Emerging Connections in Number Theory,
AMS Sectional Meeting, March, 2019.
-
13. Graduate Recruitment Symposium,
University of Michigan, March, 2019.
-
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. Arithmetic Dynamics Special Session,
AMS Sectional Meeting, Northeastern University, April, 2018.
-
4. Arithmetic Dynamics Special Session,
Joint Math Meetings, January, 2018.
-
3. Workshop on Interactions between Model Theory and Arithmetic Dynamics,
Fields Institute, July, 2016.
-
2. Colloquium,
Amherst College, April, 2013.
-
1. Pi Day Colloquium,
University of Connecticut, Mansfield, March, 2013.