Rigidity in Complex Dynamics: Multiplier Spectrum and Dynamical Andr\'e-Oort Conjecture
Algebraic Geometry
2025-11-18 v1 Dynamical Systems
Number Theory
Abstract
In this note, we present recent progress on rigidity problems in one-dimensional complex dynamics, including the proof of Dynamical Andr\'e-Oort conjecture for curves and generic injectivity of multiplier spectrum. The proofs combine ideas from algebraic geometry, Arakelov geometry and complex dynamics.
Keywords
Cite
@article{arxiv.2511.12111,
title = {Rigidity in Complex Dynamics: Multiplier Spectrum and Dynamical Andr\'e-Oort Conjecture},
author = {Junyi Xie},
journal= {arXiv preprint arXiv:2511.12111},
year = {2025}
}
Comments
To appear in the proceedings of the ICM 2026