This book grew out of a series of three Simons Symposia in 2019, 2022, and 2024, that focused on the interactions between three types of dynamics—algebraic, complex, and arithmetic—and their connections to the closely related areas of algebraic, complex, and arithmetic geometry. Dynamical systems play a key role both in pure mathematics and its applications. These meetings brought experts together from across these fields for discussions on the most significant recent developments and directions for further research.
Preface.- Dynamical Degrees, Arithmetic Degrees, and Canonical Heights:
History, Conjectures, and Future Direction.- Recent Advances on
Kawaguchi-Silverman Conjecture.- Around the Dynamical Mordell-Lang
Conjecture.- Advances in the Equivariant Minimal Model Program and their
Applications in Complex and Arithmetic Dynamics.- Dynamics of Automorphism
Groups of Projective Surfaces: Classification, Examples and Outlook.-
Questions About the Dynamics on a Natural Family of Affine Cubic Surfaces.-
Holomorphic Motions of Weighted Periodic Points.- On Slice Measures of Green
Currents on CP2.- Hölder Estimates and Uniformity in Arithmetic Dynamics.-
Entire or Rational Maps with Integer Multipliers.- Tischler Graphs of
Critically Fixed Rational Maps and their Applications.- Mirrors of Conformal
Dynamics: Interplay Between Anti-Rational Maps, Reflection Groups, Schwarz
Reflections, and Correspondences.- On Boundedness of Zeroes of the
Independence Polynomial of Tori.
