Finite orbits and canonical heights for large groups of automorphisms.

Abstract: Consider a complex projective surface $X$, with a non-abelian free group $G$ acting faithfully and regularly on $X$. It may happen that $G$ has infinitely many periodic orbits: this is the case when $X$ is an abelian surface and all torsion points are $G$-periodic. In this talk, I will describe recent results obtained with Romain Dujardin aiming at a complete classification of all such examples. The main players will be canonical heights, arithmetic equidistribution, and rigidity results in ergodic theory.

dynamical systems

Audience: researchers in the topic

BIRS workshop: Algebraic Dynamics and its Connections to Difference and Differential Equations

Series comments: The field of algebraic dynamics has emerged over the past two decades at the confluence of algebraic geometry, discrete dynamical systems, and diophantine geometry. In recent work, striking connections have been observed between algebraic dynamics and much older theories of difference and differential equations. This meeting brings together mathematicians with expertise in such diverse fields as ring theory, complex dynamics, differential and difference algebra, combinatorics and algebraic geometry. New work towards the dynamical Mordell-Lang and dense orbit conjectures as well as theorems on hypertranscendence and functional independence proven by connecting difference Galois theory, algebraic dynamics and other algebraic approaches to the study offunctional equations will be presented at this meeting.