9 dec 2021 -- 16:00
Roma Tor Vergata (online)
Seminario PRIN 2017 "Real and Complex Manifolds: Topology, Geometry and Holomorphic Dynamics"
Abstract.
In this talk, I will discuss the dynamics of post-critically finite, or PCF, endomorphisms in higher dimension. In dimension one, PCF rational maps are those with only periodic or preperiodic critical points. In higher dimension, PCF endomorphisms are endomorphisms of CPk with only periodic or preperiodic critical hypersurfaces. In spite of being really well understood in dimension one, many classical results in dimension one remain unknown in higher dimension. I will focus on the progress of generalizing the following property of PCF rational maps : every nonzero multiplier of a PCF rational map has a modulus strictly bigger than 1. I will also discuss some active directions of research about PCF maps in higher dimension.