Trevor Hyde
Assistant Professor of Mathematics and Statistics
Vassar College
thyde@vassar.edu · tghyde.github.io · 403 Rockefeller Hall, 124 Raymond Ave, Poughkeepsie, NY 12604
Research
I work in arithmetic dynamics and number theory, with excursions into algebraic geometry, combinatorics, representation theory, and topology. Recurring themes in my work include rational points in orbits, preperiodic points, and profinite iterated monodromy groups; the statistics of polynomial factorization over finite fields and their connection to the cohomology of configuration spaces; and explicit Galois theory. My recent work focuses on the arithmetic of absolute geometry.
Computational and Formal Methods
- Lean / formal verification. Designed and taught Formalizing Mathematics (Math 301, senior seminar, Spring 2025), an intensive course on the Lean 4 proof assistant (course repository). Self-taught in Lean since 2024.
- AI tools in research. Exploring the use of AI tools in my research since late 2022; regular user of Claude, ChatGPT, and Gemini. Interested in alignment and safety of AI.
- Software projects. AI-assisted coding projects on GitHub, including hwgenie (bespoke course management software), Row Reducer (an interactive row-reduction practice tool with exact arithmetic), Portalz (visualization tool for exploring branched coverings of 3-manifolds), and Ricochet Solitaire (a solitaire version of the board game Ricochet Robots).
- Computer algebra and programming. SageMath and Python, for research computation (e.g. the Sage notebook supplement to publication 7 below) and for exploratory problem sets in number theory and linear algebra courses.
Education
| Ph.D., Mathematics | University of Michigan | 2019 |
| Thesis: Polynomial Statistics, Necklace Polynomials, and the Arithmetic Dynamical Mordell–Lang Conjecture | ||
| Advisors: Jeffrey Lagarias and Michael Zieve | ||
| B.A., Mathematics, summa cum laude, Phi Beta Kappa | Amherst College | 2012 |
Appointments
| Assistant Professor of Mathematics and Statistics | Vassar College | 2023–present |
| NSF Mathematical Sciences Postdoctoral Research Fellow | University of Chicago | 2020–2023 |
| L. E. Dickson Instructor | University of Chicago | 2019–2023 |
| Moss Quantitative Fellow | Amherst College | 2012–2013 |
Grants, Fellowships, and Awards
| AMS–Simons Research Enhancement Grant for PUI Faculty | AMS / Simons Foundation | 2026–2029 |
| NSF Mathematical Sciences Postdoctoral Research Fellowship (DMS-2002176) | National Science Foundation | 2020–2023 |
| Swogger Award for Exemplary Classroom Teaching | University of Chicago | 2022 |
| Rackham Predoctoral Fellowship | University of Michigan | 2018 |
| Wirt and Mary Cornwell Prize | University of Michigan | 2018 |
| Rackham Outstanding Graduate Student Instructor Award | University of Michigan | 2018 |
| Department of Mathematics Outstanding Teaching Award | University of Michigan | 2017 |
| Robert Breuch Thesis Prize | Amherst College | 2012 |
| Post-Baccalaureate Fellowship | Amherst College | 2012 |
Publications
* denotes an undergraduate coauthor at the time of the work.
Preprints
- The arithmetic of semirings, Part I: ideals, with J. Chen*, D. Laurens*, J. Piermarini*, and H. Simons*, submitted (2026), arXiv:2607.10778.
- Rational orbits under correspondences, submitted (2026), arXiv:2605.04391.
Refereed journal articles
- Profinite iterated monodromy groups of unicritical polynomials, with O. Adams, to appear in Algebra Number Theory (2026), arXiv:2504.13028.
- Polynomials with many rational preperiodic points, with J. R. Doyle, Trans. Amer. Math. Soc. 378 (2025), no. 8, 5981–6011, arXiv:2201.11707.
- Cyclotomic factors of necklace polynomials, Acta Arith. 204 (2022), 287–316.
- Dynatomic polynomials, necklace operators, and universal relations for dynamical units, with J. R. Doyle and P. Fili, New York J. Math. 28 (2022), 534–556, arXiv:2108.09333.
- Dynamical moduli spaces and polynomial endomorphisms of configurations, with T. Blum*, J. R. Doyle, C. Kelln*, H. Talbott*, and M. Weinreich, Arnold Math. J. 8 (2022), 285–317.
- Euler characteristic of the space of real multivariate irreducible polynomials, Proc. Amer. Math. Soc. 150 (2022), 2331–2343.
- Density of periodic points for Lattès maps over finite fields, with Z. Bell*, J. Camero*, K. Cho*, C. Lu*, R. Miller, B. Thompson, and E. Zhu*, J. Number Theory 238 (2022), 951–966.
- Polynomial factorization statistics and point configurations in ℝ3, Int. Math. Res. Not. IMRN 2020, no. 24, 10154–10179.
- Liminal reciprocity and factorization statistics, Algebr. Comb. 2 (2019), no. 4, 521–539.
- Polynomial splitting measures and cohomology of the pure braid group, with J. C. Lagarias, Arnold Math. J. 3 (2017), no. 2, 219–249.
- Gauss’ hidden menagerie: from cyclotomy to supercharacters, with S. R. Garcia and B. Lutz, Notices Amer. Math. Soc. 62 (2015), no. 8, 878–888.
- Galois theory of the lemniscate, with D. A. Cox, J. Number Theory 135 (2014), 43–59.
- Small dynamical heights for quadratic polynomials and rational functions, with R. Benedetto, R. Chen, Y. Kovacheva, and C. White, Exp. Math. 23 (2014), 433–447.
- A Wallis product on clovers, Amer. Math. Monthly 121 (2014), no. 3, 237–243.
- Pre-images in quadratic dynamical systems, with B. Hutz and B. Krause, Involve 4 (2011), no. 4, 343–363.
Conference proceedings and thesis
- Factorization statistics and the twisted Grothendieck–Lefschetz formula, extended abstract, Sém. Lothar. Combin. 80B (2018), Art. 6 (FPSAC 2018).
- Arithmetic dynamical Mordell–Lang, and Noncommutative arithmetic dynamical Mordell–Lang, with M. Zieve, Chapters 5–6 of the author’s dissertation, University of Michigan (2019), available on Deep Blue.
Teaching
Vassar College
- Math 261, Introduction to Number Theory: Fall 2023 (2 sections), Fall 2024 (2 sections), Spring 2025, Fall 2025 (2 sections)
- Math 361, Modern Algebra: Spring 2024, Fall 2024
- Math 331, Topics in Geometry: Fall 2025
- Math 301, Senior Seminar: Formalizing Mathematics (Spring 2025); Representation Theory (Fall 2026)
- Math 221, Linear Algebra: Spring 2024, Fall 2026 (2 sections)
- Math 399, Senior Independent Work: Galois Theory (3 students, Fall 2024); Advanced Algebra (1 student, Spring 2025); Category Theory (3 students, Fall 2025); Algebraic Number Theory (3 students), Computational Algebraic Geometry (1 student), and Topos Theory (1 student), Fall 2026
- On sabbatical leave, Spring 2026
University of Chicago
- Math 161–162, Honors Calculus (inquiry-based learning): 2019–2020
- Math 202, Abstract Linear Algebra: Winter 2020
- Math 242, Algebraic Number Theory: Spring 2022
- Math 254, Group Theory: Winter 2022
- Math 255, Rings and Fields: Winter 2022, Spring 2023
University of Michigan
- Math 116, Intermediate Calculus: seven semesters, 2014–2018; course co-coordinator, Winter 2018 (exams and assignments for 800+ students, 30+ instructors)
- Math 115, Introduction to Calculus: Fall 2013
- Math 215, Multivariable Calculus (lab instructor): Fall 2016
Student Research and Mentoring
| URSI Mentor (Undergraduate Research Summer Institute) | Vassar College | 2025 |
| Directed Reading Program Mentor | University of Chicago | 2021–2023 |
| REU Mentor | University of Chicago | 2020–2022 |
| REU Mentor, Summer@ICERM (led to publications 7 and 9 above) | ICERM | 2019 |
| Math Circle Instructor | University of Michigan | 2019 |
| REU Mentor | University of Michigan | 2015 |
| Michigan Math and Science Scholars Instructor | University of Michigan | 2015 |
| Ross Mathematics Program Counselor | Ohio State University | 2013 |
Service and Organizing
| Co-organizer, AMS Special Session on Arithmetic Dynamics | Joint Math Meetings | January 2027 |
| Fellowship Committee | Vassar College | Fall 2026 |
| Library Committee | Vassar College | Fall 2025 |
| Co-organizer, Asprey Lecture Series | Vassar College | 2023–present |
| Co-organizer, Department Colloquium (15+ speakers hosted) | Vassar College | 2023–present |
| Speaker, DUSO lecture series | Vassar College | 2024 |
| Organizer, Let’s Talk About Math Grad School information session | Vassar College | 2023 |
| Co-organizer, No Boundaries Seminar | University of Chicago | 2021–2023 |
| Organizer, Farb and Friends Seminar | University of Chicago | 2021 |
| Co-organizer, AMS Special Session Current Trends in Arithmetic Dynamics | Joint Math Meetings | 2021 |
| Organizer, Student Representation Theory Seminar | University of Michigan | 2018 |
Referee for Proc. Amer. Math. Soc., Trans. Amer. Math. Soc., J. Théor. Nombres Bordeaux, New York J. Math., Finite Fields Appl., Int. J. Number Theory, Exp. Math., Proc. Roy. Soc. Edinburgh Sect. A, J. Combin. Theory Ser. A, Ergodic Theory Dynam. Systems, Int. Math. Res. Not. IMRN, Amer. Math. Monthly, Math. Intelligencer
Grant reviewer for the Israel Science Foundation (ISF) and the Austrian Science Fund (FWF)
Invited Talks
- Math Day Keynote Address, Colorado State University, November 2026 (upcoming)
- Number Theory Seminar, Academia Sinica, Taiwan, May 2026
- Algebra Seminar, National Central University, Taiwan, May 2026
- AG@PUI Seminar (online), March 2026
- Special Session on Arithmetic Dynamics, AMS Sectional Meeting, Boston College, March 2026
- Colloquium, Amherst College, March 2026
- AIM Workshop Dynamics of Multiple Maps, Caltech, November 2025
- Algebra/Number Theory Seminar, University of Rochester, March 2025
- Algebra Seminar, Florida State University, February 2025
- Special Session on Arithmetic Dynamics, Joint Mathematics Meetings, January 2025
- Algebra and Number Theory Seminar, Penn State University, November 2024
- Special Session on Arithmetic Dynamics, Joint Mathematics Meetings, January 2023
- Special Session on Arithmetic Dynamics, AMS Sectional Meeting, University of Utah, October 2022
- Arithmetic Dynamics International Online Seminar (ADIOS), February 2022
- Algebraic Dynamics Seminar, Harvard University, February 2022
- Number Theory Seminar, Oklahoma State University, March 2021
- Algebraic Geometry Seminar, University of Washington, February 2021
- Math Club, University of Connecticut, October 2020
- Special Session on Arithmetic Dynamics, Joint Mathematics 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
- Complex Analysis, Dynamics, and Geometry Seminar, University of Michigan, March 2019
- Combinatorics Seminar, University of Michigan, February 2019
- Algebra Seminar, Wayne State University, January 2019
- Combinatorics Seminar, University of California, Berkeley, November 2018
- Geometry/Topology Seminar, University of Chicago, November 2018
- Formal Power Series and Algebraic Combinatorics (FPSAC), Dartmouth College, July 2018
- Combinatorial and Additive Number Theory Workshop, CUNY Graduate Center, May 2018
- Special Session on Arithmetic Dynamics, AMS Sectional Meeting, Northeastern University, April 2018
- Special Session on Arithmetic Dynamics, Joint Mathematics Meetings, January 2018
- Interactions between Model Theory and Arithmetic Dynamics, Fields Institute, July 2016
- Colloquium, Amherst College, April 2013
- Pi Day Colloquium, University of Connecticut, March 2013
Last updated September 2026. PDF version.