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One of my primary research interests is understanding properties about the Mandelbrot set and Julia sets, such as their Hausdorff dimension.
In preparation for such work, I've been studying parabolic implosion in one- and two-variable complex dynamics and researching finite-point configurations in compact sets using Newhouse and Yavicoli thickness.
Papers
Papers
Published
Published
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. Triangles in the plane and arithmetic progressions in thick compact subsets of R^d, with Krystal Taylor, 2025. (arXiv:2506.00571)
In Progress
In Progress
2. Quantitative results on arithmetic progressions in compact sets of sufficiently thick subsets of R^d, with Krystal Taylor.
1. Generalized parabolic implosion, with Katelynn Huneycutt and Liz Vivas.
Research Awards
Research Awards
Research Associate, NSF Training Grant (RTG) DMS-2231565, Spring 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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