Research

Lately, I have been keeping myself busy thinking of renormalization theory in complex dynamics.

Papers

A priori bounds and degeneration of Herman rings with bounded type rotation number, 58pp. arXiv:2302.07794
Rigidity of J-rotational rational maps and critical quasicircle maps, 58 pp. arXiv:2308.07217
Hyperbolicity of renormalization of critical quasicircle maps, in preparation.

Slides for lectures on Herman rings and Herman curves
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
Quadratic-like renormalisation in holomorphic dynamics. Master’s Thesis. pdf
Holomorphic dynamics and several complex variables: a brief summary in preparation for orals. pdf

Rigidity for 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
Introduction to Renormalization Theory. Graduate Student Seminar, Stony Brook University, Sept 2023.
From Herman Rings to Herman Curves. Complex Analysis and Dynamics Seminar, CUNY, Mar 2023. slides
A Priori Bounds and Degeneration of Herman Rings. Dynamics Seminar, Stony Brook University, Nov 2022.
A Priori Bounds and Degeneration of Herman Rings. On Geometric Complexity of Julia Sets IV, Banach Center, IMPAN, Aug 2022. video
(Dynamics of) Quadratic Polynomials. Graduate Student Seminar, Stony Brook University, Dec 2021
What Is… An Orbifold? Graduate Student Seminar, Stony Brook University, Feb 2021. video