Trevor Hyde

Research

My research interests include arithmetic dynamics, arithmetic statistics, geometry of configuration spaces, Galois theory, and algebraic combinatorics.

Papers are listed newest first. See also my arXiv listing.

Publications

  1. The arithmetic of semirings, Part I: ideals with Jay Chen, Dorien Laurens, Jasper Piermarini, and Harriet Simons Preprint, submitted for publication (2026) arXiv:2607.10778 pdf
  2. Rational orbits under correspondences Preprint, submitted for publication (2026) arXiv:2605.04391 pdf
  3. Profinite iterated monodromy groups of unicritical polynomials with Ophelia Adams To appear in Algebra & Number Theory (2026) arXiv:2504.13028 pdf
  4. Polynomials with many rational preperiodic points with John R. Doyle Transactions of the AMS, Vol. 378, No. 8 (2025), 5981–6011 arXiv:2201.11707 pdf
  5. Cyclotomic factors of necklace polynomials Acta Arithmetica, Vol. 204 (2022), 287–316 pdf
  6. Dynatomic polynomials, necklace operators, and universal relations for dynamical units with John R. Doyle and Paul Fili New York Journal of Mathematics, Vol. 28 (2022), 534–556 arXiv:2108.09333 pdf
  7. Dynamical moduli spaces and polynomial endomorphisms of configurations with Talia Blum, John R. Doyle, Colby Kelln, Henry Talbott, and Max Weinreich Arnold Mathematical Journal, Vol. 8, No. 2 (2022), 285–317 doi:10.1007/s40598-022-00197-z pdf
  8. Euler characteristic of the space of real multivariate irreducible polynomials Proceedings of the AMS, Vol. 150 (2022), 2331–2343 pdf
  9. Density of periodic points for Lattès maps over finite fields with Zoë Bell, Jasmine Camero, Karina Cho, Chieh-Mi Lu, Rebecca Miller, Bianca Thompson, and Eric Zhu Journal of Number Theory, Vol. 238 (2022), 951–966 doi:10.1016/j.jnt.2021.10.009 pdf
  10. Polynomial factorization statistics and point configurations in ℝ3 International Mathematics Research Notices, Vol. 2020, No. 24 (2020), 10154–10179 doi:10.1093/imrn/rny271 pdf
  11. Liminal reciprocity and factorization statistics Algebraic Combinatorics, Vol. 2, No. 4 (2019), 521–539 pdf
  12. Factorization statistics and the twisted Grothendieck–Lefschetz formula Extended abstract, Séminaire Lotharingien de Combinatoire, Vol. 80B (2018), Art. 6 (FPSAC 2018) pdf
  13. Polynomial splitting measures and cohomology of the pure braid group with Jeffrey C. Lagarias Arnold Mathematical Journal, Vol. 3, No. 2 (2017), 219–249 doi:10.1007/s40598-017-0064-z pdf
  14. Gauss’ hidden menagerie: from cyclotomy to supercharacters with Stephan Ramon Garcia and Bob Lutz Notices of the AMS, Vol. 62, No. 8 (2015), 878–888 pdf
  15. Galois theory of the lemniscate with David A. Cox Journal of Number Theory, Vol. 135 (2014), 43–59 pdf
  16. Small dynamical heights for quadratic polynomials and rational functions with Rob Benedetto, Ruqian Chen, Yordanka Kovacheva, and Colin White Experimental Mathematics, Vol. 23 (2014), 433–447 pdf
  17. A Wallis product on clovers The American Mathematical Monthly, Vol. 121, No. 3 (2014), 237–243 pdf
  18. Pre-images in quadratic dynamical systems with Ben Hutz and Ben Krause Involve, Vol. 4, No. 4 (2011), 343–363 pdf
  19. On the number of rational iterated pre-images of −1 under quadratic dynamical systems American Journal of Undergraduate Research, Vol. 9, No. 1 (2010), 19–26 pdf

Doctoral Thesis

Polynomial statistics, necklace polynomials, and the arithmetic dynamical Mordell–Lang conjecture, University of Michigan (2019). Advisors: Jeffrey Lagarias and Michael Zieve.

Invited Talks