Algebraic Dynamics seminar: Some properties of cohomologically hyperbolic maps

A cohomologically hyperbolic map is a self-dominant rational map on an algebraic variety that satisfies certain conditions on dynamical degrees. For example, polarized endomorphisms and birational maps on surfaces with non-trivial first dynamical degree are cohomologically hyperbolic. Cohomologically hyperbolic maps (are expected to) enjoy nice arithmetic dynamical properties, such as having Zariski dense orbits, having dense and bounded height set of periodic points.  I will explain some theorems in these directions, some are work in progress.