Research

My current research is complex dynamics, mostly in one variable. (Watch this talk for an accessible introduction to the field.)

Papers

  1. Hyperbolicity of renormalization of critical quasicircle maps, 88pp. arxiv:2405.09008
  2. Rigidity of J-rotational rational maps and critical quasicircle maps, 58pp. arXiv:2308.07217
  3. A priori bounds and degeneration of Herman rings with bounded type rotation number, 58pp. arXiv:2302.07794

Others

  • Slides for lectures on Herman rings and Herman curves
  • PhD Thesis. (basically a combination of 1,3, and half of 2…) pdf
  • Critical quasicircle maps: realization and rigidity. Poster presented in the ‘Inaugural CNAM-Fields Nonlinear Days: Renormalization and Friends’ conference at the Fields Institute. pdf
  • From Herman rings to Herman curves. Poster presented in the ‘Complex Dynamics in the Tropics’ Conference at IMPA. pdf
  • Master’s Thesis. pdf

A few recent talks

  • Critical Quasicircle Maps. Dynamical Systems Seminar, Boston Univesity, Oct 2024. slides
  • Rigidity of Rotational Dynamics. AMS Sectional Meeting, UW Milwaukee, April 2024. slides
  • Critical Quasicircle Maps. Workshop on Dynamical Systems and Related Topics, UMD, April 2024. slides
  • Degeneration of Herman rings. Geometry & Topology Seminar, Brown University, Jan 2024. slides
  • From Herman Rings to Herman Curves. Quasiworld (Online) Seminar, Nov 2023. slides
  • From Herman Rings to Herman Curves. Complex Analysis and Dynamics Seminar, CUNY, Mar 2023. slides
  • A Priori Bounds and Degeneration of Herman Rings. On Geometric Complexity of Julia Sets IV, Banach Center, IMPAN, Aug 2022. video