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I am interested in understanding properties of fractal sets, so I study complex dynamics and geometric measure theory.
Complex Dynamics: I research parabolic bifurcation to calculate conditions for Moebius transformations to converge under iteration.
Geometric Measure Theory: I study Newhouse thickness to determine sufficient conditions for compact dust sets to contain finite-point configurations.
Papers
Papers
Published
Published
2. Triangles in the plane and arithmetic progressions in thick compact subsets of R^d, with Krystal Taylor.
Canadian Journal of Mathematics. Published online 2026:1-41.
1. A Reidemeister type theorem for petal diagrams of knots with Leslie Colton, Cory Glover, and Mark Hughes.
Topology and its Applications, 267:106896, 2019.
Preprint
Preprint
1. A non-autonomous model for parabolic implosion, with Katelynn Huneycutt and Liz Vivas.
Preprint, 2026.
In Progress
In Progress
2. A Lavaurs-type convergence theorem, with Liz Vivas.
1. Quantitative results on arithmetic progressions in compact sets of sufficiently thick subsets of R^d, with Krystal Taylor and Alexia Yavicoli.
Research Awards
Research Awards
Research Associate, NSF Training Grant (RTG) DMS-2231565, Spring 2026.
JMM 2026 Graduate Student Travel Grant, January 2026.
AWM-NSF funds to travel to 2025 Joint Mathematics Meeting, NSF DMS-2113506.
Special Graduate Assignment, The Ohio State University's Mathematics Department, Spring 2025.
Tibor Radó Graduate Fellowship, The Ohio State University's Mathematics Department, 2021-2022.
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