Rigidity in Complex Dynamics: Multiplier Spectrum and Dynamical André-Oort Conjecture

Abstract

In this note, we present recent progress on rigidity problems in one-dimensional complex dynamics, including the proof of Dynamical André-Oort conjecture for curves and generic injectivity of multiplier spectrum. The proofs combine ideas from algebraic geometry, Arakelov geometry and complex dynamics.

To appear in the proceedings of the ICM 2026