Research

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

I specialise in three renormalization theories (1. quadratic-like, 2. irrationally indifferent fixed points, 3. Herman curves) and their consequences on rigidity, universality, and the geometry and topology of fractal sets.

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

Some slides

  • Renormalization Theory of Herman Curves. Geometric Complexity of Julia Sets VI, Bedlewo, Aug 2025. slides
  • Area of the Postcritical Set. Topics in Complex Dynamics 2025, U of Barcelona, June 2025. slides
  • Rigidity of Rotational Dynamics. AMS Sectional Meeting, UW Milwaukee, April 2024. slides
  • From Herman Rings to Herman Curves. Quasiworld (Online) Seminar, Nov 2023. slides
  • A Priori Bounds and Degeneration of Herman Rings. On Geometric Complexity of Julia Sets IV, Bedlewo, Aug 2022. video

Others