Overview: I am primarily interested in many classical problems (and their variants) in geometric measure theory. As a result, I'm happy to try to approach them using whatever tools are available. Lately, most of my work has been on "effective dimension", which is a concept that emerges in computability theory, specifically the study of algorithmic randomness. Effective dimension is a measure of the asymptotic complexity of a single point, but through the point-to-set principle of Jack and Neil Lutz, this quantity gives information about the Hausdorff and packing dimension of sets. Jack and Neil's original paper on this topic is a great introduction.
Papers and Preprints: Links are provided, and feel free to click the title for a more informal introduction and overview, as well as additional related material.
Dimension of pinned distance sets for semi-regular sets (with Don Stull). Submitted. Arxiv link: https://arxiv.org/abs/2309.11701
Bounds on the dimension of lineal extensions (with Ryan Bushling). To appear in Journal of Fractal Geometry. Arxiv link: https://arxiv.org/abs/2404.16315
Pinned distances of planar sets with low dimension (with Don Stull). Submitted. Arxiv link: https://arxiv.org/abs/2408.00889
Universal sets for projections (with Don Stull). Submitted. Arxiv link: https://arxiv.org/abs/2411.16001