Research
My current research is complex dynamics, mostly in one variable. (Watch this talk for an accessible introduction to the field.)
Papers
- Hyperbolicity of renormalization of critical quasicircle maps, 88pp. arxiv:2405.09008
- Rigidity of J-rotational rational maps and critical quasicircle maps, 58pp. arXiv:2308.07217
- 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