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My main interests are in holomorphic dynamics in one variable, in both rational and transcendental dynamics. My current focus is on transcendental Thurston theory, particularly the behavior of Thurston pullback operators. On a broader level, I am interested in 'dynamically' approximating transcendental maps by rational ones, and exploring relationships between various transcendental families. 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.
In October 2023, I was a Program Associate at the SLMath/MSRI semester in Algorithms, Fairness and Equity.
During June-August 2023, I worked as a research intern at the MGGG Redistricting Lab at Tufts University.
During Jan-May 2022, I was a Lauter Program Associate at the MSRI semester in complex dynamics.
Dynamical approximation of postsingularly finite exponentials, arXiv, 2023
Dynamical approximations of postsingularly finite entire maps (joint with Prochorov, Reinke), Submitted; arXiv, 2023
Embedding unicritical connectedness loci, Accepted; arXiv, 2022
A solution to the degree-d twisted rabbit problem (joint with Winarski), Submitted; arXiv, 2022
Marked cycle curves for quadratic polynomials and rational maps (joint with Davis, Stoll and Tiozzo)
VoteKit, a Python package for research on alternative voting systems I helped develop during my time at MGGG.
Midwest Dynamical Systems Early Career Conference, The Ohio State University, May 2024
AMS Spring Central Sectional Meeting: Special Session on the Panorama of Holomorphic Dynamics, April 2024
17th Annual Bloomington Geometry Workshop, Indiana University Bloomington, April 2024
University of Illinois Chicago Dynamics Seminar, January 2024
Boston University Dynamics Seminar, January 2024
Joint Mathematics Meetings: Special Session on the Mathematics of Decisions, Elections and Games, January 2024
Quasiworld Seminar (Online), December 2023
Cornell University Dynamics Seminar, November 2023
University of Michigan Complex Analysis, Dynamics and Geometry Seminar, November 2023
AMS Fall Southeastern Sectional Meeting: Special Session on Ergodic Theory and Dynamical Systems, October 2023