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My main interests are in holomorphic dynamics, spanning both rational and transcendental dynamics. At the moment I am focussing on problems in Thurston theory, which is the study of topological branched self-covers of an oriented surface with certain restrictions on dynamics. I use tools from topology, complex analysis and Teichmüller theory.
Lately I have also been studying algorithmic fairness in voting systems - specifically the use of geometric and analytic tools to understand alternative voting systems such as ranked choice voting and Borda, and techniques for generating random ranked ballots.
Along with Ryan Goh, I organize the BU Dynamical Systems seminar.
Vanessa Matus de la Parra and I also run the virtual Baby Mandelbrot Set Meetings for early-career complex dynamicists.
Embedding unicritical connectedness loci, Conform. Geom. Dyn. 28 (2024), 131-164, doi.org/10.1090/ecgd/389
A solution to the degree-d twisted rabbit problem (joint with Winarski), Ergodic Theory and Dynamical Systems. Published online 2025:1-16. doi:10.1017/etds.2025.137
Dynamical approximations of postsingularly finite entire maps (joint with Prochorov, Reinke), Submitted; arXiv
Dynamical approximation of postsingularly finite exponentials, arXiv
A cell decomposition for marked cycle curves (joint with Davis, Stoll and Tiozzo), arXiv
Donnay et al., (2025). VoteKit: A Python package for computational social choice research. Journal of Open Source Software, 10(109), 7477, https://joss.theoj.org/papers/10.21105/joss.07477
In August 2025, I helped organize the DKO Workshop and Summer School on Transcendental Thurston Theory in the UK.
During July and August 2025, I visited the Tata Institute of Fundamental Research and the Chennai Mathematical Institute in India.
In July 2026, I will be attending the Complex Dynamics: Interactions and Influences programme at INI, Cambridge, UK.
Tufts University Dynamical Systems and Ergodic Theory Seminar, December 2025
University of South Alabama Colloquium, November 2025
AMS Fall Central Sectional Meeting: Special Session on Algebraic and Arithmetic Dynamics, Saint Louis University, October 2025
Social Choice: Theory and Computation, An Interdisciplinary Conference on Voting, Representation, and Districting, Wellesley College, October 2025
Harvard University Informal Seminar: Dynamics, Geometry and Moduli Spaces, September 2025
DKO Workshop and Summer School on Transcendental Thurston Theory, The University of Manchester, August 2025
Chennai Mathematical Institute Colloquium, August 2025
Tata Institute of Fundamental Research, July 2025
JHH80 Dynamical Developments: Degenenerations of Flat Surfaces and Rational Maps, Institut de Mathématiques de Toulouse, June 2025
Topics in Complex Dynamics 2025: Connections to Geometry and Analysis, Universitat de Barcelona, June 2025
Degeneration Techniques for Rational Maps, Warwick Mathematics Institute, May 2025
New England Dynamics Seminar, April 2025
Brandeis University Everytopic Seminar, April 2025
Here is my CV.