Abstract:
We will discuss the stability of holomorphic dynamical systems under perturbation. In dimension 1, the theory is now classical and is based on works by Lyubich, Mané-Sad-Sullivan, and DeMarco. I will review this theory and present a recent generalisation valid for families of endomorphisms in any dimension. Since classical 1-dimensional techniques no longer apply in higher dimensions, the approach is based on ergodic and pluripotential methods.

Bio-Sketch:

Fabrizio Bianchi completed his undergraduate studies at the Scuola Normale Superiore of Pisa, Italy. He received his PhD in 2016 from both the Institut de Mathématiques de Toulouse and the Università di Pisa, under the supervision of François Berteloot and Marco Abate. He then joined Imperial College London, first as a Chapman Fellow and later as a Marie Curie Fellow. From 2019 to 2023, he was a CNRS researcher, affiliated with the Laboratoire Paul Painlevé in Lille, France. He is currently an Associate Professor in the Department of Mathematics at the University of Pisa.