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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, to appear in the Canadian Journal of Mathematics, 2025. (arXiv:2506.00571)
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. Generalized parabolic implosion, with Katelynn Huneycutt and Liz Vivas, preprint available upon request, 2025.
In Progress
In Progress
1. Quantitative results on arithmetic progressions in compact sets of sufficiently thick subsets of R^d, with Alexia Yavicoli and Krystal Taylor.
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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