This book is concerned with the dynamics of rational transformations of projective varieties and meromorphic transformations of compact Kahler manifolds. Four main viewpoints are developed. The first article describes the geometry of the varieties which admit a rational transformation with interesting dynamical properties; the geometry constrains the existence of such dynamical systems, but interesting examples with rich dynamics are described. The second article explains how complex analysis, potential theory, and Hodge theory can be married with methods from dynamical systems to describe the stochastic properties of meromorphic transformations of Kahler manifolds. Then, arithmetic aspects of algebraic dynamical systems are described in a third article; in particular, equidistribution theorems in diophantine geometry and dynamical systems are analyzed and compared. The fourth article describes the basics of $p$-adic dynamics in one variable.
... 2015 Peter S. Ozsváth, András I. Stipsicz, and Zoltán Szabó, Grid Homology for Knots and Links, 2015 Vladimir I. Bogachev, Nicolai V. Krylov, Michael Röckner, and Stanislav V. Shaposhnikov, Fokker–Planck–Kolmogorov Equations, ...
In this volume, the author gives a unified presentation of some of the basic tools and concepts in number theory, commutative algebra, and algebraic geometry, and for the first time in a book at this level, brings out the deep analogies ...
With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.
This book originated in the idea that open problems act as crystallization points in mathematical research. Mathematical books usually deal with fully developed theories.
Duke Math. J. 59 (1989), no. 3, pages 785–801. [9] Cassels, J. W. S., Flynn, E. V. Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2, London Matematical Society Lecture Note Series 230, Cambridge University Press (1996).
... Mathematics, 2017 Erica Flapan, Allison Henrich, Aaron Kaestner, and Sam Nelson, Editors, Knots, Links, Spatial Graphs, and Algebraic Invariants, 2017 Jeffrey Bergen, Stefan Catoiu, and William Chin, Editors, Groups, Rings, Group Rings ...
This volume contains the proceedings of the Ninth International Conference on Finite Fields and Applications, held in Ireland, July 13-17, 2009. It includes survey papers by all invited speakers as well as selected contributed papers.