Random Algebraic Dynamics in Complex Dimension 2

Explore a 43-minute conference talk on random algebraic dynamics in complex dimension 2, presented by Romain Dujardin for the International Mathematical Union. Delve into recent findings on the dynamics of automorphism groups in real and complex projective surfaces, covering topics such as stationary and invariant measures, orbit closures, and finite orbits. Examine basic examples, open problems, and various techniques from complex and algebraic geometry, as well as arithmetic random, holomorphic, and dynamical systems. Learn about properties of non-elementary groups, linear examples like Abelian and Kummer surfaces, and groups generated by involutions. Investigate Wehler's (2.2.2) surfaces, their propositions, and main results. Study the classification of automorphisms, including elliptic, parabolic, and laxodromic maps. Understand finite orbits for non-elementary groups, stationary and invariant measures, and proofs of the stiffness theorem and equidistribution. Access accompanying slides for visual support of the presented concepts.

Intro
Properties of non-elementary groups
Linear examples: Abelian and Kummer surfaces
Groups generated by involutions
Main example: Wehler's (2.2.2) surfaces
Wehler's (2.2.2) surfaces Proposition
Main results for the Wehler family
Summary - Outline
Action on cohomology / Classification of automorphisms
Classification of automorphisms: elliptic maps
Classification of automorphisms: parabolic maps
Classification of automorphisms: laxodromic maps
Finite orbits for non-elementary groups
Stationary and invariant measures
Proof of the stiffness theorem
Proof of equidistribution