I do number theory and arithmetic dynamics.

Here is my curriculum vitae.

Shabnam Akhtari, Liubomir Chiriac, Holly Swisher, and I organize Oregon Number Theory Days, a triannual number theory seminar rotating between Oregon State University, Portland State University, and the University of Oregon.

John Caughman and I organize the Portland State University Combinatorics and Number Theory Seminar.

From Fall 2013 to Spring 2018, I was the faculty mentor of the math Club.

Research:

• The distribution of a-numbers of hyperelliptic curves in characteristic three, with Jeffrey Lin Thunder and Colin Weir.
  (Submitted for publication.)
• Periodic points of rational functions of large degree over finite fields.
  (To appear in Trans. London Math. Soc.)
• Preperiodic points of polynomial dynamical systems over finite fields, with Aaron Andersen.
  Int. J. Number Theory 20 (2024), no. 9, 2307–2316. (Here is the arXiv version.)
• Periodic points of polynomials over finite fields.
  Trans. Amer. Math. Soc. 375 (2022), no. 7, 4849–4871. (Here is the arXiv version.)
• The cycle structure of unicritical polynomials, with Andrew Bridy.
  Int. Math. Res. Not. IMRN (2020), no. 23, 9120–9147. (Here is the arXiv version.)
• A probabilistic heuristic for counting components of functional graphs of polynomials over finite fields, with Elisa Bellah, Erin Tannenbaum, and Noah Walton.
  Involve 11 (2018), no. 11, 169–179. (Here is the arXiv version.)
• Dynamically distinguishing polynomials, with Andrew Bridy.
  Res. Math. Sci. 4 (2017), no. 13, 1–17. (Here is the arXiv version.)
• A weighted Möbius function.
  Discrete Math. 340 (2017), no. 9, 2200–2207. (Here is the arXiv version.)
• Some finite abelian group theory and some q-series identities.
  Ann. Comb. 20 (2016), no. 2, 361–371. (Here is the arXiv version.)
• Random matrices, the Cohen-Lenstra heuristics, and roots of unity.
  Algebra Number Theory 9 (2015), no. 1, 149–171. (Here is the arXiv version.)
• Abelian surfaces over finite fields with prescribed groups, with Chantal David, Zachary Scherr, Arul Shankar, Ethan Smith, and Lola Thompson.
  Bull. London Math. Soc. 46 (2014), no. 4, 779–792. (Here is the arXiv version.)
• Graph components and dynamics over finite fields, with Ryan Flynn.
  Int. J. Number Theory 10 (2014), no. 3, 779–792. (Here is the arXiv version.)
• The a-numbers of Jacobians of Suzuki curves, with Holley Friedlander, Beth Malmskog, Rachel Pries, and Colin Weir.
  Proc. Amer. Math. Soc. 141 (2013), 3019–3028. (Here is the arXiv version.)