English

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

R2 v1 2026-07-01T07:38:53.177Z