Research, Papers, and Preprints

Most of my research has been in complex dynamics, focusing on transcendental dynamics, the dynamics of non-polynomial entire functions.

Papers and Preprints

  • Transcendental Julia Sets with Fractional Packing Dimension. Published 2021 in Conformal Geometry and Dynamics. Journal Link. The contents of this paper formed my Ph.D thesis. Examples of transcendental entire functions whose Julia set has packing dimension strictly between 1 and 2 are constructed, the first examples of this kind.

  • Interpolation of Power Mappings (Joint work with Kirill Lazebnik). Submitted to Revista Matematica Iberoamericana. arXiv Link. Inspired by the techniques of "quasiconformal folding", we give a procedure for creating entire functions modeled off of monomials on large annuli.

  • Transcendental Julia Sets with Minimal Hausdorff Dimension (Joint work with Kirill Lazebnik). Submitted to Ergodic Theory and Dynamical Systems. arXiv Link. A sequel to the paper above, we construct examples of transcendental entire functions with Hausdorff dimension 1 Julia sets with new topological phenomena.

  • A Jordan Curve that cannot be Crossed by Rectifiable Arcs on a set of Zero Length. Preprint. arXiv Link. A better title: "World's Worst Jordan Curve" or "A Very Twisty Jordan Curve". We construct a Jordan curve in the plane such that any rectifiable arc that crosses this curve intersects it on a set of positive length.