TOPICS IN ALGEBRAIC DYNAMICS

Abstract

In algebraic dynamics one typically studies discrete dynamical systems on algebraic varieties. Such a system is given by an endomorphism or a rational delf-map of a variety X. Based on some joint works with Meng, Shibata, Wang, Xie, Zhang and Zhong, I summarise three topics in algebraic dynamics: (1) classification of projective varieties admitting non-isomorphic endomorphisms; (2) interaction between arithmetic geometry and algebraic dynamics; (3) automorphism groups of algebraic/analytic varieties.